Widely available in the USA, you will probably only encounter valet parking in more exclusive hotels and clubs in the UK, and at places - such as airports - that offer a (paid) valet parking service.
If you unexpectedly encounter complimentary valet parking, react with aplomb. Hand your keys to the attendant and walk away without a backward glance; never apologise about the state of your car, or plead with them to drive carefully.
When they return the car, and if you are satisfied with the service (i.e. you haven't been made to wait too long and your precious vehicle is none the worse for wear), then offer them a tip (minimum £1).