tosh.
'Our streets' is a reasonable chant from a bunch of people who've occupied the streets in protest, whether about cars, student fees or something else. The street(s) have been taken over and the people who've taken them are right in claiming they're 'our streets'.
'Our Brixton' is very different.
and while there are aspects of class involved here I don't think deploying class as part of this discussion will achieve anything other than division. Neither existing communities nor any of the wave after wave of incomers are delineated by class, and this notion that all incomers are m/c is just lazy stereotyping.