There's only one thing slightly more competitive than medicine and that's VetMed...
Rightly or wrongly, Sports Science is not going to be seen as the most academically rigorous first degree, and you will be in direct competition with both school leavers with a raft of A* at GCSE and A level and graduates in experimental sciences with similar qualifications. I'm not trying to be negative here, just realistic as it would be irresponsible to write some spiel filling you with false hope.
If you're serious about an application for VetMed, then I would suggest chemistry A level is an absolute must. You'd be advised to contact the few VetMed schools there are to enquire about this, and whether they'd be happy to accept an A level post degree (most are, so long as you get an A/A* at the first sitting). A good result in A level chemistry, and a very strong score in the UKCAT and you've started to look like a serious candidate...