Contrary to popular belief, Sherlock Holmes was a very tactile person. He liked soft, comfortable clothes. He would touch, taste, and smell chemicals he had no business touching, tasting, and smelling. He was also, and his brother can attest to this, a notorious cuddle-slut.
While Mycroft was uncomfortable with touch (and Sherlock had several theories about that), Sherlock was a personal space invader. As a child he insisted on holding Mycroft's hand whenever they went somewhere, demanded hugs from his mother and his brother (his father had not reacted well to his toddler trying to climb him like a tree so Sherlock never went to him for cuddles). As an adult he still wanted to hold Mycroft's hand whenever they went anywhere together, but their relationship was not what it had been, so he never did. All he had wanted to do after that horrible night at the pool was light a fire, put on his softest jimjams, and crawl into John's lap to sleep for a day or two. He didn't, of course, but he wanted to.
When he pulled John out of the lab at Baskerville, he felt a strong urge to hug the man and not let go. This was strange. Sherlock never wanted to give comfort. The feeling only got stronger after seeing John's reaction to his reaction to Irene Adler. He found John's jealousy fascinating and deeply flattering, though he wasn't sure why.
Standing on top of St Bart's that day was the worst thing Sherlock had ever done, or felt. Hearing John, seeing him, only caused that feeling deep inside of him to plunge to his stomach and twist about his organs, making him light-headed and causing tears to rise. Of course, the tears were a side-effect of the drug Molly gave him so he wouldn't actually die, but still.
Five years later, when he returned with boxes full of information on Moriarty, more than enough to clear his name, and Lestrade's (he felt very bad about the man's demotion, thought he'd make it up to him), John punched him in the face. Yet, he avoided Sherlock's nose and teeth again. Sherlock spent a week apologizing, making tea, buying groceries, before John told him he was being weird and would the real Sherlock Holmes please stand up.
John Watson was a strange individual.
About a month after his return, he succumbed to his urge to sweep John up into a great big hug and just not let go. He wasn't sure what had brought it on. John hadn't minded, he just told him that perhaps a crime scene wasn't the best place to, ah, cuddle. Anderson was slowly dying of laughter in the background.
When they returned to 221B, John asked why Sherlock had hugged him. When Sherlock said he'd wanted to since John moved in, and that he supposed his resolve wasn't what it used to be after six and a half years, John just laughed and said he was welcome to do it any time he liked.
It only made sense that, six months later, he succumbed to his urge to kiss the living daylights out of on Dr John H Watson.
(Fortunately, it wasn't as a crime scene.)