I think your main difficulty would be getting work in the UK when competing with "home grown" graduates, because although your degree is as valid & rcvs-worthy as anyone elses, employers won't be likely to have direct experience with a grad of your uni and would probably prefer to hire someone "tried & tested" if at all possible. Once you've got your 1st job under your belt it shouldn't be so much of an issue, though.
Just for interests sake, when you say the rcvs recognises your degree, does that mean you don't have to sit further exams to work as a vet in the uk? (If Slovakia is part of the EU I guess it does mean that, but I cba checking a list of EU member states.) Outside the EU it might get more awkward. I know an English guy who qualified DVM from SGU in Grenada (Caribbean, as opposed to Grenada, Spain) and has had to sit an English profiency exam (in addition to the RCVS written & practical exams) to be allowed to register!