Boroughs that will remain largely affordable by 2016 include Hillingdon, Ealing and Hounslow to the West; Enfield and Waltham Forest to the North; Newham, Barking and Dagenham and Havering to the East, and Lewisham, Bexley and parts of Croydon to the South.
Boroughs that will have the highest proportions of unaffordable property include Kensington & Chelsea and Westminster as well as Islington, Camden and Tower Hamlets.
Shelter is warning that the cuts could change the make-up of London for decades to come.
Shelter chief executive Campbell Robb said: "This research shows that in just five years’ time, the number of London neighbourhoods affordable to those on local housing allowance will more than halve, with swathes of the capital becoming largely unaffordable.
"This will mean tens of thousands of households priced out of their homes and communities, creating concentrations of poverty across the city and adding to the already significant levels of homelessness and overcrowding in the city.
"The 53,000 claimants in London who are in work may also be forced to move away from their jobs, so these proposals could ultimately act as a disincentive to work."
The picture beyond 2016 could get even worse: Government plans to link housing benefit levels to the Consumer Price Index from 2013 will deliver an even bigger blow to people on local housing allowance.
Between 1999/2000 and 2007/08 median rents in London increased by 65%, compared to just a 17% increase of the CPI.
Robb said: "Breaking the link between housing benefit and the cost of housing will see rents quickly outstrip the amounts people are receiving. While the impact will not be immediate, over time this is likely to make the situation starkly worse and even more neighbourhoods unaffordable.
"While Shelter supports reform of housing benefit, cuts on this scale are going to have a devastating economic and social impact on London and we urge the Government to urgently rethink them."
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