if harry hart is the world-renowned chef at an italian restaurant in london then eggsy's the new waiter who's meant to work there only for the summer before he goes on his backpacking trip to southeast asia. harry's picky and strict attitude irks eggsy at first and he regularly complains this to his best bud, roxy, the bartender who also recommended eggsy for the job.
but like one time eggsy has to return to the restaurant because he forgets his things (keys?), he sees harry feeding the stray cats bacons and it is such. an. adorable. sight? he can hardly believe it. another time he sees harry giving candy to daisy, the little girl is waiting for eggsy after work, and his heart melts just a tiny bit.
however, he knows for sure he's been wrong about harry the entire time is when harry stays back and helps him clean the kitchen: the chef is trying to come up with a new dish and offers it to eggsy to try. his warm brown eyes wide with expectations coupled with his dimples revealed by his delighted smile when eggsy earnestly compliments him and enthusiastically gives him two thumb-ups? that's what clinches it for eggsy.
one could say it is love at first bite.