That's really interesting, because in the region of the US I came from, I never once saw the cake shared out amongst the guests. I mean, I've been to a lifetime of US weddings. More than I could ever count and I can't remember a single one where the guests ate the actual cake. In fact, many cakes now use styrofoam or rice crispie treats under several of the layers to cut down on costs since they won't be served anyway. The bride and groom cut the cake and ate a bite, but nobody else did.
Each wedding I've gone to here, however, has cut up the cake and shared it with it's guests. I've been looking at that as a more UK thing to actually eat the cake (although it's sometimes eaten later at home as others said).
As others said though, do whatever you want. It's your wedding, and different traditions from other places are becoming more and more prevalent in UK weddings anyway.