That’s actually a good budget to work with in the borough of Sutton.
You could look at Worcester Park - similar commute to current, Cheam Common Inf&Juniors are top schools and easy for drop offs on the way to work. Slight black hole for secondary (Blenheim and Glenthorne take some and you can hope for a grammar place). If you buy a bit further from the station (15min walk) towards Cheam High, you’ll get yourself into that catchment and within walking distance of the leisure centre and the lovely Nonsuch Park. Near the station, there’s a Waitrose and a bunch of other shops, cafes and restaurants.
Then, Carshalton Village is lovely with the Thameslink from Carshalton and LB train from Beeches. Victoria trains too. There are nice cafes and pubs, a theatre, an ecology centre, lots of young families and events. There’s also a huge leisure centre and a library and tons of greenery (parks, and even lavender fields etc).
If you’re Catholic or CofE, you could look in Wallington - fab period properties and LB train but a bit pants for schools unless faith or DC get into grammars.
Sutton is another one. Thameslink, LB and Victoria trains. Biggish town centre with lots of amenities (cinema, play park and trampoline park, sports clubs, shops, restaurants etc). The south side is the really lovely, leafy bit with the countryside within walking distance. The North side is a bit more mixed but plenty of nice roads, save and great schools anyway. Extra nice if you find a place within walking distance of Cheam Village which is lovely but pricier.