I can highly recommend Ffiona's at 51 Kensington Church Street. This charming, intimate and totally English restaurant is a short walk from Kensington Palace, Hyde Park and Kensington High Street tube station.
The food is excellent and unpretentious, service caring and delivered most times in person by Ffiona, the gracious and engaging owner.
I always go for the Welsh lamb and sticky toffee pudding ( best in UK). Many other options including vegetarian and vegan.
This is a true neighborhood restaurant with many devoted clients and friends. You'll love your experience here. I have been going for 15 years since I first stayed in the neighborhood and discovered a card in my flat's directory.