Re:
That's a how long is a piece of string type question, rather like, what's the best car for £500?
For that budget you can get a new bike, but your money will get you a lot more second hand. It all depends on what you want the bike for, how often you are going to ride it, and how far.
In very general terms, I'd look in the classifieds here, one ebay, gumtree, any cycle recyling charities that you may have in your area and all the usual places. You should be able to find something to suit in a decent tubeset like Reynolds 531.
I'm sure others here will have some sensible suggestions; good luck with your search.