First of all, I have to come to the defence (spelled with a 'c') of the actors' British accents. Unless your name is Henry Higgins, I don't think you'll mind what you hear here. Now Keanu Reeves doing Shakespeare or Julia Roberts doing Mary Reilly, THOSE are bad accents. In "Caffeine" the two American fakers had me fooled enough to think they were actual Brits.
Now on to the movie. Like many good Brit comedies, the overall plot isn't as important as the witty criss-crossing of subplots. Like a clever stage play, that and some good acting is all you need. The whole story is set in a restaurant: the dining room, kitchen, and back balcony. Basically it's "a day in the life" of a bunch of oddball characters working and dining in a cafe.
The stories revolve mostly around romantic/sexual relationships and the absurd situations they create. Like a good Shakespearean romp... or the 70s sitcom "Three's Company", all the mayhem is the result of misunderstandings, awkwardness and overreactions. The film starts out somewhat tame, but as it progresses and we get to know each character, they seem to become increasingly insane. One of my fave segments was the meek vegetarian girl who was subjected to an excruciating blind date with a gun-toting macho man. By the time the movie is near its end, anything goes.
If you like dialogue-driven films that feel like plays, such as "Death at a Funeral" (original version 2007), "Le dîner de cons" (original version 1998), "My Tiny Universe" (2004), "Deathtrap" (1982) or even the classic "Who's Afraid of Virginia Woolf" (1966), I think this movie will be worth your time.