Don't listen to what the Leicester Square-eating tourists say. London is home to several of the best restaurants in the world!
I've found one of the most cost-effective ways of experiencing the best food (and yes, it is an experience at some of these places!) is to take advantage of the set lunch menu. A 3-course menu runs from anywhere to £25 to £35 a person (which is a fabulous deal when you consider other menu options).