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I know it's a Tory area - I live in Bickley.
The Tory vote, however is largely the elderly population who are obviously on the way out...Chatterton Village (where I live) is a nice area with good transport links, local (non chain) businesses and a large park. You can also still buy a fully detached house with driveway and garden for less than £600k which is a minor miracle within the m25.
That whole area, of the Bromley umbrella which includes bickley, chislehurst, Petts wood, Bromley common etc is very tory tastic as op said. If thats an issue move to a less affluent area where the demographic are more likely to vote labour, and far less likely to have the middle class shops.