All the stats from vet schools can be found on their individual websites or there is a the same info on AAVMC website under the individual school info. The numbers and stats of international students accepted vary greatly, just like with any US school. Of course, if you are competing against 300 international applicants for 50 spots in a UK school versus 500 out of state applicants for 15 spots in a US school...the odds would be in your favor. Check out AAVMC for the actual numbers.
I agree though that less US students apply overseas, actually putting the odds in your favor, but you still have to have a competitive application. Almost everyone in my class had acceptances other places. Many of them US schools.
It really varies depending on who is applying that cycle. I have a friend that got into 2 US schools but neither Edinburgh nor RVC. You need to be competitive like Packen said.