This thread really highlights the challenge of living in London for people that aren't on high incomes. To be fair South West London has always been desirable so has higher income families than the average. But even then I think it got magnified with the doubling of house prices 10 years ago. I wonder if a house price crash would mean these areas return to a more mixed demographic.
Someone up thread asked how I know the split in demographic in Putney. It's because I'm a parent and have lived there for 20 years or so. More and more I'm coming to the conclusion that Putney, Barnes, Richmond, Wimbledon, Surbiton, Wandsworth, Clapham etc are some bizarre bubble - essentially becoming what Fulham used to be. I.e. populated by lawyers, accountants, doctors, management consultants, famous people or business owners. There are people that don't seem to understand that people can be on less than 50k salaries! I'm exaggerating a bit, there are a few... but usually only one parent in the couple ;)
There are areas of deprivation (Alton Estate - Roehampton, Winstanley estate in Clapham) and some areas that I would consider more normal (Castelnau estate, Dover House estate, possible Putney Vale and Roehampton Vale). Cheap houses start at 650k, so rule out people on lower salaries if they haven't had help.
The recommendations for slightly further out places seems sensible to me. Furzedown, Streatham, Earlsfield, Worcester Park, Kingston, Epsom do make more sense. I quite like Kingston personally, the shopping centre is nice, has the river and Richmond park for cycling. Mini holland approach to cycle infrastructure, and easy out to Surrey and the off-road route out there. It is relatively cheaper (and more normal) because public transport to central London isn't great. Also it has its own local employment so not entirely London-centric.
I have family in the South West UK so being able to get out of London in the car is a real bonus. If you mean SW UK rather than SW London for your PiL then do try to get somewhere with decent access to the A3 or A4 to drive out quickly. Putney to Guildford is 30 mins. Clapham to Putney is often that long due to traffic. I bought a car when SW trains failed to reserve seats for on a Christmas Eve train. It was an horrendous journey stood until Salisbury!