More than 800 were left without a home in October after their claims were decided by the Home Office and they were given just days to leave their accommodation, according to new statistics.
Local authorities across the capital warned on Thursday that the total of 846 homelessness presentations could surge even further as the Home Office seeks to clear the claims backlog, as cold weather sets in.
London Councils, the cross-party body which conducted the research, said October's figure was already an increase of 39 per cent on September’s figure of 609.
The figures include those who are rough sleeping but also "hidden homeless", such as those sleeping on someone else's floor.
Officials say the problem is being exacerbated by too little notice given by the Home Office before refugees need to vacate hotels or hostels.
However, a Home Office spokesperson said those ordered to vacate accommodation because their claim had been successfully decided were given 28 days' notice.
Cllr Grace Williams, London Councils’ Executive Member for Communities, said: "No one wants to see refugees becoming homeless after leaving Home Office accommodation, but this is happening at an alarming rate across the capital.
"Boroughs are deeply concerned by the situation, which will only get more dangerous as winter sets in. Those granted asylum need adequate support for settling in the UK, yet too often are forced into sleeping rough on the streets.
"At a time when London already faces enormous and unsustainable homelessness pressures, the government urgently needs to prevent this happening.”
Cllr Williams said a longer notice period of 56 days was "crucial" and that additional funding was needed for councils.
Kathy Mohan, chief executive of Housing Justice, which supports rough sleepers, said the situation was "desperate".
"The churches, mosques, and temples in our network are seeing rising numbers of refugees and asylum-seekers approaching them for help, asylum decision letter in hand, with nowhere to sleep, and no idea how to get the support they need,” she said.
"We help where we can but many are resorting to rough sleeping."
A Home Office spokesperson said: "We are committed to ensuring asylum claims are considered without unnecessary delays.
"Once someone is informed that their asylum claim has been granted, they get at least 28 days notice to move on from their asylum accommodation.
"Support is offered to newly recognised refugees by Migrant Help and their partners, which includes advice on how to access Universal Credit, the labour market and where to get assistance with housing.
"We are working with local authorities to help communities manage the impact of asylum decisions as the legacy backlog reduces."
The warning comes after data published last week showed that 60,580 households in London were living in temporary accommodation in June - an increase from last year’s end-of-June total of 56,340.