[matthewking]

They call this "health tourism" and its a fairly regular subject that comes up whenever NHS budgets are discussed, in reality though I believe latest figures put it at about £300m /year (0.3% of the NHS budget).

I don't know how easy it is to do what you describe but some people evidently do it. I imagine if you're an EU citizen you can come right in but if you're non EU you might have some more difficulty.