OP, have you ever thought to look south of the river, just for comparison?
For instance, Wimbledon Village would be much more expensive, but in the edge of that you might find something to suit in your price range (eg more into Wimbledon proper or Southfields / Raynes Park way)?
Putney is great and more central too - with massive plus if the river and great state primaries? It’s more expensive that MH, but there are houses at that sort of price?
Sheen has big houses and is a little cheaper (because of no tube). Adjacent to Richmond Park and sits between Putney and Richmond?
Barnes is truly like a village in a bend if the Thames with a duck pond and village green and the whole shebsng. Very expensive, but you might still find a house under £2 million. 15 mins into Waterloo on main line trains which are very frequent, or Hammersmith tube is there (bridge reopening to pedestrians in July apparently).
Or Richmond itself? A bit further out, but it’s beautiful there and and it’s a town in its own right. On the District Line but also fast main line connections.
Even try places like St Margaret’s or Teddington as you can get more for your money there (probably similarly priced to MH)? But the river that way is gorgeous.
Also, for that type of house, you could look at Chiswick perhaps? Acton borders offer more for your money.
Just a few ideas as you say you’ve not been in London that long. all these. Very family-friendly areas and I think SW London feels a bit more laid back because of proximity to the Thames. It’s very green and lots of parks. It is more expensive but you can assure your DH that this whole area is particularly stable in terms of house prices.
Parsons Green or Fulham may also be worth a look?