Surely if you wanted to live in the CW area you could? In the past 15 years I have worked on around 3,000 flats in the area to the south of it, of which only a relatively small proportion are the dreaded 'social rented' type. There are plenty to buy with prices aimed at those who work in the new city (or just want to buy to leave). Most of those developments contain shared equity flats for those just starting out on the fiscal ladder.
Re: overt social cleansing of inner city areas.
I thought that went away with Shirley Porter and her 'Building Stable Communities' activities in the 1980's? I recall she resigned and then fled the country when it came to light that she had been using public money to change the political colour of Westminster by moving out the Labour voters which was considered uncool even then.