Areas to consider for housing

Moving this summer with husband and two children (9 months and 2.5 at the time of move) and have no clue where to start when it comes to finding housing. I’d love somewhere with great nursery options, parks/playgrounds, walkable daily errands(cafes, casual dining, etc.), decent commute(>60min) to Battersea, and ideally we wouldn’t have a car but not a dealbreaker if best to have one. Any ideas for areas we should consider and look into?