It appears to be the same belt (or "doughnut") effect discussed more generally with respect to other elections in (Greater) London. Basically Greater London is more than the [core] city, which itself is quite Labour and Remain oriented.
Here's the EU referendum results on a London map:
Image from polimapper; alas their [color] scale is a bit coarse.
A better map in terms of color scale, but alas with lower geographical resolution:
The BBC has ward-level data, but alas they don't depict it on a map, however they do offer this analysis for some (Greater) London areas:
Ealing and Hounslow are neighbouring multi-ethnic boroughs in the west of London with large Asian populations, where - in contrast to the national picture - non-white ethnicity was associated with voting Leave, particularly in Ealing. Both boroughs shared a varied internal pattern of prosperous largely white areas voting strongly Remain, poorer largely white areas preferring Leave, and the Asian areas tending to be more evenly split.
Ealing voted 60% Remain, with Southfield ward hitting 76%, but in contrast the Southall wards which are over 90% ethnic minority were close to 50-50.
In Hounslow the richer wards in Chiswick in the east of the area voted heavily Remain (73%), but the poorer largely white wards at the opposite western end in Feltham and Bedfont voted Leave (64-66%). Osterley and Spring Grove was also 63% Leave, the highest Leave vote in any individual ward in the UK with a non-white majority for which we have data.
The south London borough of Bromley narrowly voted Remain. Those parts which did not do so by a significant margin were the Cray Valley wards, largely poor white working class areas; and Biggin Hill and Darwin wards, locations to the south which contain more open countryside and lie outside the built-up commuter belt.
In Croydon in south London, places which voted Leave by substantial amounts were New Addington and Fieldway, neighbouring wards with large council estates.
So the poor & white suburban areas seem to have voted consistently enough for Leave in Greater London as they did nationwide. The Asian voting pattern differed in London than elsewhere though.