There’s a post that says there’s only one time in the whole movie that Harry touches Eggsy and as deep as I may be in this trash heap I’ve only seen the thing twice so I can neither confirm nor deny it’s veracity. But what if it’s because Harry is actually an extremely tactile person? Hear me out….
He loves to touch and be touched. He knows that when he cares for someone that there will be no end to how much he wants to simply feel them beneath his fingers, the warmth of their skin, the pace of their heartbeat. But he is a gentleman and that intimacy is reserved for those closest to him. So he does everything he can to keep his hands to himself in public.
Once they acknowledge their feelings for each other Eggsy becomes addicted to it. To the way Harry’s hands will rest on his hip while they cook together, how he will hook their fingers together at dinner, the caring way he idly runs his fingers through Eggsy’s hair while they are curled up on the couch reading on the rare quiet evening they manage to find time to themselves.
Of course he still very much keeps his hands to himself in public, self aware enough that if he gives in to a simple touch he will likely want more despite the inaoropriate nature of what he desires. That is simply not a part of their relationship that is available for public consumption. At first Eggsy is very confused, and a little hurt, because he thinks that maybe Harry doesn’t want to acknowledge “them” in public.
But because he’s madly in love and very much a capable adult Eggsy brings it up as soon as he realizes that it bothers him. And Harry feels terrible that he has hurt him so and they make a compromise that whenever Eggsy want to reach out for Harry’s contact he will gladly accept it, and make up for every time he had wanted to reach out himself the moment they’re alone.
Eggsy, flushed and breathless after the first time Harry keeps his promise, figures he got the better end of the deal.