i was in london recently and used hedonists guide to london and their eat london guidebooks for the the best restaurants in london. best book i've used so far for less touristy places. i don't have a smart phone but i'm pretty sure they have an app. my fave was Cecconi's - way out of my budget but it had champagne on tap!
Well, for a true London experience you should go to The Ivy! It is very classic and you will have unforgettable time there! I also think it is not so pricy