'a group of people' OP - that is 8 million people!
Also I think you have a skewed and frankly inaccurate view. I know some phenomenally wealthy (think millions and millions in the bank) people in London (they're lovely, unassuming people, actually) and trust me when I tell you that the majority of middle-class people in London do not have lives like these people, the sorts of lives I think you may be imagining.
Most 'middle class' people around here, at least, while obviously being fortunate enough not to be on the bread line, are just very ordinary people with demanding jobs, difficult bosses, huge mortgages to pay (that they might well rather not pay, but can't avoid if they need to work in London; many people do), stressful and crowded commutes every day, etc etc. The idea that middle-class SW Londoners are all quaffing champagne and calling their children Tarquin, or whatever scenario it is you might imagine, is ludicrous.
I think what you are maybe thinking of is the sorts of lives that my millionaire aquaintances have: full-time nannies, housekeepers, cooks, no money worries, Petit Bateau clothing for their children, huge Range Rovers and several foreign holidays a year.
Not a single 'middle class' person from SW London that I know of has a life anything like that. We, for example, drive a very old car, struggle with our mortgage each month and are forgoing holidays for the foreseeable future as we are saving for school fees for our DD. We don't buy new clothes for ourselves (me and DH) unless we have to. We are extremely fortunate, obviously I would never deny this, but we have big outgoings due to our mortgage (and DH HAS to work in London) and we want to send DD private and so we economise. Most people I know are doing similar things.