That depends, to some extent, on your definition of "British". 14% of the UK population is part of so-called "ethnic minorities", and they may find some "traditional" British food unacceptable. Try to feed pork to a muslim and he'll probably be highly upset. That means that about 3% of the "British" population do not eat pigmeat (or other "banned" foods).
Until a food contamination scandal 2 years ago, we didn't think we'd eat horsemeat (unlike much of Europe), but apparently we have been.....
We don't eat dogs or cats (although cooking and eating the latter would probably be a good thing).
There is a thriving business exporting ducks feet to China - we eat the ducks, but never the feet - apparently though, there are sufficient ex-pat Chinese in London nowadays for a small market to exist.
People are often surprised at the range and quality of food now available in the UK. We've come a long way from the "meat and two veg" cooked to death in the 1950s and 1960s.
Part of the reason for that is the influx of new British citizens.