Someone found me whilst googling “Vegetarian members of the UK Conservative Party”
I’m intrigued now. I don’t know of any. I do know lots of veggie Lib Dems, but not sure if I can think off the top of my head whether any of them are in the public eye.
Niles's Blog 
Alan Clark was. But he is, of course, dead.
There are quite a lot of Veggie conservatives! As a Conservative Cllr, Ward Chairman and Tory activist of over 20 years I always do a veggie option when I organise a fund raising function.
I had an old Ward Chairman who was big into the WWF – I could not visit without being forced to buy a raffle ticket to save the panda.