For working in Southwark I'd go for Battersea and cycle. I used to live in Nine Elms and cycled to the City every day - it's generally a very nice cycle ride along the river, you keep fit, save money and and your commute isn't at the mercy of signal failures and RMT strikes. That area is nicer to live in than to visit, the park is lovely and the new restaurants and shops around Battersea Power Station are fab. You're a 10 min cycle from Chelsea as well - psychologically you're far away, but practically you're very close!!
In London your commute governs so much about your quality of life that I would definitely choose a worse house for a better commute. Oh and unless you have a dedicated parking space, sell at least one of your cars, probably both, and join a car club if you need to or rent one on weekends.