You can kind of date it into 3 (somewhat overlapping) blocks,to my way of thinking, which is the "Bohemian" (for want of a better all-round term) block of settlement where the squatters and the "arty types" colonised Brixton because it was cheap, cheerful and inclusive. You could roughly date this from the '70s until the mid-'90s, and it included people buying because you could still get "bang for buck" in terms of the number of bedrooms your money would buy, if you didn't mind some of the local peculiarities.
You then had a "mainstreaming" block, which you could date from the early '90s to around 2012, where Brixton became more of a mainstream housing destination for people not deterred by folk-myth and hysteria, where a lot of people bought or rented because it made financial sense to, and who came to love the local cultures. As with the previous block, this was fairly slow and steady, although it also saw the loss (to development) of several community assets such as Cooltan.
From roughly 2010-ish (would probably have been a little earlier but for das finanzkreis) gentrification has hyper-accelerated. rather than the "slow and steady" change of the previous two blocks - which although they displaced people, tended to displace to nearby locales - gentrification in Lambeth in general - and Brixton in particular - has been fast and brutal, with the local authority leading the way in that brutality with the clearance/eviction of short-life tenants from suddenly-valuable town-centre properties, and the minimisation of their obligations to those they displaced. Speculative buying of property is also a borough-wide (and city-wide) problem, as is the development of "luxury homes" for sale - it changes expectations and markets. What has also driven this is the realisation by various commercial entities of those changed expectations, and their attempts (as diverse as Lexadon's property rentals and Shrub & Shutter's cocktails in a jamjar) to cash in on it. Short-termist profit-making is triumphing over long-term community interests and needs - Brixton is being made over in the image of a group of people who have little interest in the place or the communities, only in the profits realisable, or the social capital accrued from living somewhere "edgy".
The above is a fairly well-simplified overview.
