We – two adults and a 5-y-o and a 2-y-o) had a wonderful stay at Robert's house in Kensington. The location was just perfect: only a short walk to the nearest underground station, as well as the Kensington Gardens (Princess Diana's playground and memorial fountains were both a hit) and the shops of Kensington High Street (esp. the Whole Foods for buying food for home). There's a nice, family-friendly pub Elephant & Castle right around the corner too, as well as a traditional English restaurant Maggie Jones's nearby.
The flat is great for a small family. The bedrooms are just spacious enough, and the living room gives space for kids to play in with new toys from Hamley's. The bathtub is the one thing the small ones remember about the apartment, of course. But it's also nice for adults to unwind after a long day.
The kitchen is functional – don't expect to score Michelin stars with the cooking equipment – and everything you need to cook a quick lunch between destinations. The underground takes you fast to the Kensington museums or the heart of the city. Uber works well as well.