Advice for people in the U.S. is usually to eat sweet potatoes and squashes (or just ordinary white potatoes). In the UK, you can't always find all of those, but you can find parsnips and swedes -- and there are always bananas. And West Indian food stores might have plantains, which would be good.
Robb Wolf has a very similar regimen to the Primal Blueprint:
I've heard him say on his podcast that he trains fighters and helps them with diet, and he does Brazilian Ju-Jitsu himself. Robb has a kick boxer on his staff:
So, yeah, this diet is totally suitable for a fighter.