Outright benefits tourism is probably marginal. I would guess that low wage/hours working + tax credits is very attractive. Overall, if I was stuck in the back end of Romaina, I'd be looking at health care and standard of living in the rest of the EU and shipping out.
Greece? The problem is not solved or contained. Greece has several hundred billion in debt, zero chance of paying it back, and has rendered the ECB technically bankrupt. At the next whiff of a crisis, this will blow again. If they had lanced it 3 years ago, we would have had a 90 billion write off, it would have hurt, but it would have been controlled. Now it will be uncontrolled, because it will happen when the central banks are at their weakest. What they should have done is boot Greece out of the Euro, and taken the hit.
On the trade deficit, our balance of trade with the EU is a disaster. So there is zero incentive for the EU to cut us off - indeed, they will be desperate to keep us in. They have more to lose than us. I'm not saying it is all going to be easy, but the 'EU will cut us out and make trade really hard' meme is pure scaremongering.