This is an overall 'wouldn't it be nice/interesting if people were more sensible' AU. The focus is more on worldbuilding than plot, with how things could have ended up this way instead of as in canon.
The title is a reference to a Diana Wynne Jones book written well before HP about a boy who is brought to the home/government office building of the most powerful wizard in Britain and takes classes with other magical children in an alternate universe where everyone knows magic exists.
Of course Harry believed in magic. Everyone in England believed in magic.
Of course they did: Merlin was one of the founding heroes of the high kingdom that made England England, the protector of King Arthur. England was protected by magic to this day, like during the Blitz, how bombs kept falling on places that had already been bombed and people somehow survived without a scratch.
Everyone knew that people in hospitals got better around Halloween, to the point the NHS let cancer patients from the rest of the EU come around then, since there usually weren't that many people that sick in England. It got them a lot of money.
The pagans might believe that it was the spirits of ancestors coming to check up on their descendants during the harvest festival instead of witches on broomsticks, but everyone agreed that either way, it was magic.
There was an old lady across the street, Ms. Figg, with tons of cats, which meant she might be a witch and so everyone was very respectful to her.
Aunt Petunia had lovely witch-themed jewelry that she wore to remember Harry's mum. She told him and Dudley about his mum in a hushed voice by candlelight, how she was a witch and brewed potions that cured people and had even married a wizard like Merlin. How Harry might grow up to be a wizard and then the Evans would have two witches in the family, and since Dudley's aunt was a witch he should be proud and needed to get married and give Petunia grandchildren because whether or not he was a wizard, there was magic in his blood and he might be the proud father of another witch.
At this point, they were all pretty sure that Harry was a wizard. Either that or his parents' spirits were watching out for him, which would be just as good.
The trouble was that wizards were supposed to be all wise and noble, so Aunt Petunia didn't let him get away with anything and he had to study more than Dudley, and herbs and stars and stuff too, because there was a wizard school and his Mum had to learn a lot about wizard stuff in a hurry because she hadn't had the right education growing up and his Aunt didn't want him to struggle and get looked down on.
Dudley had extra lessons and stuff too, because that was only fair, but he got to learn martial arts and compete in junior league tournaments already. Being a wizard who didn't know how to do magic yet didn't get you trophies the way being a little knight did. Harry felt that was hardly fair.
Then the day came that Aunt Petunia had marked on the calendar, and there was a real live owl that let him feed it the fillet mignon Uncle Vernon had bought special. They gave his reply to the owl, and the next day there was another letter asking when they wanted to have a real life witch or wizard come over to tell them things. Aunt Petunia whispered to them that she could tell Harry what he needed to know and take him to get his school things because of his Mum, but did he mind letting Dudley meet a real live witch?
Of course not! This meant Harry got to see one sooner too.
The witch was a wizard, a handsome silver-haired man with a knightly bearing that made Harry and Dudley look at each other thinking, 'A wizard knight!' So cool!
He knew Aunt Petunia, which instantly made Harry's aunt ten times cooler, and apologized to her about coming instead of a professor, but they had so many young witches and wizards this year that the professors were swamped visiting people who didn't have relatives who knew about magic and Albus hadn't wanted to keep Lily's family waiting.
He also had the paperwork for Harry to attend wizard summer school so he got to explore the wizard school before actual classes started and learn about how a proper wizard acted. It sounded so much less boring than the class Petunia made them go to to learn the waltz and foxtrot and act like Proper Young Gentlemen with the word wizard attached! Also he got to go there through the fireplace!
And they got to go to the wizard shopping district.
Every town had herb shops and a place where people could buy old-fashioned brooms and cauldrons and books on old-fashioned English cooking, before the Empire when everything became tasteless roast beef that let the French make fun of them. Every ice cream parlor had flavors like Dragon's Blood and Halloween Pumpkin and Witch's Brew. Tons of kids had wands for playing magic, and Harry had tried to cast tons of spells he made up with his, hoping something would work.
This place had a wand shop with wands that had sparks come out! And a flying broom store with a broom that had a chain on it for kids to try if they hadn't gotten to fly on a broom before.
They'd gone to the bank with real goblins first, though, so Uncle Vernon could exchange some money and Aunt Petunia could get the money for Harry's things out of his trust vault. Then the man they were with apologized, saying he needed to get something and they could wait here or they could ride with him through the caverns and it was wicked.
Getting fitted for wizard robes might have been boring, but they were wizard robes and there was a real wizard in there who guessed that Harry must not have grown up a wizard because Draco knew everyone (and that was the coolest name every) and without Harry getting a word in edgewise said that he was attending the summer school to help set a good example and Harry should come to him if he needed help with proper behavior because it was his family duty to look after the common people. Like a wizard knight, even if he was a bit snooty!
"Ah, Arthur!" he heard when he got out of the clothes shop.
"You asked me to meet you, my lord?"
"No need to be so formal, I'm not wearing that infernal judge's wig at the moment. Vernon, this is Arthur Weasley. He's the head of the Muggle Technology office, and he has a keen interest in your technologies and manufacturing techniques that made him a good pick for the job of studying how to apply magic to them responsibly and keep things like teapots some witch enchanted to pour tea for her old Mum from ending up in the general population and giving someone a heart attack. Arthur, this is Vernon Dursley."
"I remember you from the wedding!" Arthur said, smiling brightly. "You married Lily's sister, yes?"
"Yes," Uncle Vernon said, holding out a hand. "I'm sorry I didn't get a chance to meet you then."
He chuckled. "Don't worry, I didn't have eyes for anyone but Molly at my wedding either."
"Vernon is the head of a drill manufacturing plant."
"The making of tools used to make tools!" Arthur grinned, practically sparkling. "I'd love to hear about your work." His face fell. "I wanted to stay in contact with you and Petunia afterwards, but…"
Vernon waved away the apology. "Better safe than sorry dealing with those continental wizards… no offense," he told the old man quickly.
"No offense taken. Why do you think so many of us came to England?" he rolled his eyes.
"Should I assume that you're here because of…"
Vernon nodded, but the old man held a finger to his lips and Arthur nodded quickly, looking a little embarrassed. "It is a relief, but I won't say anything more."
"Oh, don't say that," Vernon said, clapping him on the back. "It's not often someone says they want to hear me talk about my work. Far too many people take drills for granted."
"No!" Arthur looked shocked.
When they went into the bookshop Vernon and Arthur remained outside with the old wizard to keep chatting about work. Harry caught Dudley rolling his eyes a moment before Petunia said, "Why don't you two look around for something interesting while I get Harry's school things. Just remember, Dudley, your book has to be something that it's alright for you to show our friends."
"Yes Mum," he said quickly, before darting a glance at Harry and the two of them dashed for the fiction section, passing a bushy-haired girl their age staring in delight as books flew around her.
"And I'll take this," the old wizard said once the clerk was done ringing up Petunia's purchases. "Here you go, boys," he said, handling The Tales of Beedle the Bard to Dudley. "Now I believe there's a knight in at least one of these stories."
Dudley opened the book and started flipping through it as they walked out of the store, Harry leaning to look over his shoulder.
"Why didn't you just recommend it to me?" his aunt asked.
"Albus wanted me to pick up something as interest on all those late birthday presents, and he loves that book."
Most of the adult wizards at the school dressed in black robes, same as the uniform cloak. Except for Hagrid, who wore tough clothes to deal with the invisible animals and everything.
The headmaster wore a cloak all colors of the rainbow and there was a smiley-face and a peace sign button pinned to his hat, so the first time Harry saw him he knew he was a hippie.
There were a lot of them in England, what with Stonehenge and the magical tradition and everything. His aunt and uncle didn't quite approve of them, but they made Uncle Vernon's headache tea and the one kind of yogurt Aunt Petunia liked. Harry quite liked the commune in the town commons because they encouraged them to play with the animals and he'd ridden a horse once (only once: they were big and lots of other kids wanted to have a go).
"I'd love to tell you, 'Welcome to Hogwarts!' But I can't say that quite yet, you see. You'll be here on the first day of school: right now we're smuggling you in so you can get a sneak peak." The headmaster held a finger to his mouth, as though he was telling them to keep a secret. "This first week, you'll be assigned to groups with professors showing you around and filling you in on whatever they think is good for you to know before you come to class. After that, in the mornings you'll have lessons and after lunch you'll be able to pick who to go with. Ms. Pince will escort a group to the library every day; Hagrid will be taking you to explore more of the grounds; Argus will be teaching you how to navigate the school; and Professors Sprout and Snape will be available to take you to the greenhouses and potions lab to work with you to make sure you know how to stay safe around magical plants and potions. I highly encourage everyone to go with each of those groups at least once. It's very easy to get turned around when the moving stairs turn around, you see."
Harry didn't want to be late for class when it was magic class.
"Professor Lupin, Madam Hooch and the other professors will also be taking groups some days: they'll let you know their schedules. We may also have some mysterious guests!"
"Alright everyone, time to put on your blindfolds," said Hagrid. "They're all on? Here we go." He rang a gong, the sound reverberating in the huge stone chamber. A door grated open, and Harry heard something moving closer. "Now, this 'ere is Slytherin's basilisk, the protector of Hogwarts."
"Even more tiny wizards than last year," the snake hissed, sounding pleased. "My hatchlings must be having large, healthy clutches."
"Who wants to feed her?" Hagrid asked, sounding excited.
Harry thrust his hand up in the air before realizing that Hagrid couldn't see him. "Me, sir!"
"Ah, Harry!" Hagrid said cheerfully. "Reminded me of your dad, you did. Come over towards me, and I'll hand you a hunk of venison." Harry did, and Hagrid turned him around afterwards and pushed at his back. "Walk a bit closer to her, and hold it up in the air. This'll give her a chance to smell you too, so she knows you're one o' hers."
Harry did, and stopped when he felt cool air on his face.
"A Potter," the snake said thoughtfully.
"Yes, my name's Harry Potter," he told her.
"You can speak a civilized tongue, child?"
"I'm sorry ma'am, I don't know what you mean."
She hissed softly, thoughtfully. "I smell a bit of Salazar's magic on you, but not his blood. Curious." The venison was lifted from his hands, and he heard her gulping it down. "Come visit me again, hatchling."
"You can understand her when she talks?" Hagrid asked.
"Yes? She wants me to visit her again. I understood a python at the zoo once too. Is that weird?" Harry asked him, as some of the kids behind him began to whisper.
"It's a rare gift, that is. One of the founders of Hogwarts had it, it's how he was able to get a basilisk to protect our school. Raised her himself, ol' Salazar did. Didn't care a bit about how dangerous she was," Hagrid said proudly. "But you'll hear more about the founders in Social Studies. Right, now back up Harry, time for someone else to get the chance to introduce themselves."
In this universe, Hagrid is a Slytherin, extremely skilled at finding loopholes he can squeeze his pets through and with the ambition to carry on Scamander's work. He helps out with the legal stuff for magical animal rights' groups.