SW still has some young hip and trendy parts, and also I think it's a bit of a cliché to think them all as wine drinking Fulham or rugby supporters. Roehampton for example used to be rough council estate territory then the uni students and some property developers took over. Brentford is also pretty mix of wwc and crossing into Brent Indian territory, Merton and Wombleland despite the rep because of the tennis has working class areas. Massive Korean community in Motspur Park.
So not homogeneous.
Homogeneous can be seen as a relative thing. SW London is homogeneous compared to, say, some areas of Central London; the Stockbroker Belt is, taken together, homogeneous compared to SW London; and rural Norfolk and Lincolnshire are homogeneous compared to the Stockbroker Belt.
So it's really yes and no.