This is not really a suggestion for your parents' dinner, because I think it needs to be something that is really British and/or French or Italian. But I recently had an amazing meal in a restaurant just next to Southwark tube, called "Baltic". It was Eastern European/Scandinavian food, more Polish than anything else, and it was magical. Really, really well done, expertly prepared and inventively seasoned, it blew every preconception I had ever had about Eastern European food out of the water. Plus a vodka menu of 50 rare vodkas. The service was exceptional (for London) - really pleasant and really quick.
Have you thought about the Jamie Oliver place?
What about the River Cafe? That is definitely a good choice for a one-off dining experience, though it would be too rich for my blood on a regular basis. I have all their cookbooks, and I like them, though I think many people think it is overpriced for what you get.