Harry Hart is not a gentleman.
Well, he is; he believes in manners and chivalry and dressing for the occasion, but that's really it.
He's never liked the other shit that people tell him make a gentleman: he hates discussing art, and even if Merlin does tell him that Tosca is the supreme example of why opera is such a fine art form, Harry still thinks it's shit that is only mildly better because everyone dies and can't torture him anymore. He'd rather listen to rock music, and it's good luck that his house is soundproofed and Mrs. Dabney, the cranky old woman next door with an opinion about everything and everyone—all the same, of course; everything and everyone is simply awful—can't hear him singing along to AC/DC.
He knows how to use each utensil properly, including all seven knives, and can correctly guess what a meal will be based solely on those observations. But if Harry had a choice, he'd much rather stop at the burger place around the corner and use his hands to scarf the thing down. He licks his fingers, too. Dinner forks don't make one a gentleman.
And why would he watch the news when he's got more than enough bad shit to watch in his own life? He sees enough of that on missions and deals with the dregs of society weekly—has experienced the worst of people in ways the average person can't even imagine, killed and nearly been killed himself more times than he can count. In Harry's opinion, watching the news is just like being at work. No, if he has a choice, he'll turn on Big Brother UK or The Apprentice. He'll never admit to liking them, though, not upon penalty of death. He knows, objectively, he's still seeing the dregs of society, but there's a lot less blood at the bottom of this particular barrel.
He holds doors for people because that's just common courtesy. He's not doing it to be a gentleman any more than saying "please" and "thank you" does. He wears suits because they're comfortable, sort of a security blanket, and a well-tailored suit fits better than anything else, makes him feel cosier than a pair of warm pyjamas.
Harry will never admit he doesn't care much for wine. He can determine the age of a good bottle based solely on its hue, and list off the qualities of the aroma before his first sip. He went undercover once and successfully passed himself off as a world-class master sommelier, after all. But he'd rather have a pint of Guinness, or the cheapest ale he can buy at the pub. The company there doesn't often have the same stick up its arse as those wine-drinking circles, too.
In short, Harry Hart is not a gentleman. He even drinks milk right from the carton when he's home alone, and often wishes those pound notes in his wallet were for more interesting things than tipping doormen.
But he thinks maybe he ought to try to be one, once he sees how Eggsy Unwin looks up to him and copies his actions. Even Merlin's started teasing him about his young doppelganger. So Harry stands up straighter, shows the boy how to tie a bow tie, and promises to teach him how to adjust his arrogance into affability.
Perhaps being a gentleman isn't the worst thing Harry Hart could be.