Thought I remembered something from the remain camp that we had a veto to stop further membership increases 
Yes, admitting new countries into the EU requires the unanimous approval of all existing members. So we (currently) have a veto, as do Cyprus, Greece etc. It only takes one of these to vote against and it won't happen. I simply can't see Cyprus or Greece agreeing membership at the moment regardless of how much arm twisting Merkel does. These things don't normally get aired in public - they're all sorted out behind closed doors, and agreements reached, and then there is a public announcement of a 'unanimous' approval. So basically, if anyone says they're going to veto it, it's said in private and it never gets to a vote.
However, before we even get to that stage, Turkey has to meet (IIRC) 20 criteria for admission. At the last count, they only met one of those criteria. It'll be years (probably decades) before they meet all the requirements.
There is no chance of Turkey being 'in' within the next 10 years.