In a "clear sign the system is broken", no children were transferred from London through the Home Office's National Transfer Scheme during the first quarter of 2019, according to London Councils' report Unaccompanied Asylum Seeking Children: A Place of Safety.
This is putting the capital's councils under unsustainable pressure, with fears that it could put in jeopardy their ability to care for these children, claims the group, which represents the 32 London borough councils.
This year's rate has fallen from 33 transfers in the equivalent period in 2018, the report states.
It claims the low number is against a backdrop of growing numbers of unaccompanied children arriving in the capital and a claimed £32 million local authority funding shortfall last year.
The group is calling for the Ministry of Housing, Communities and Local Government, the Home Office and Department for Education to agree reforms to the scheme to put it on a sustainable footing.
There were about 1,800 unaccompanied asylum seeking children in the care of London boroughs in 2018/19, making up at least a third of all such children across England, and about 2,900 care leavers who were once unaccompanied children.
London and Kent are under the most pressure as children are most likely to arrive through southern ports and airports, and the system was set up in 2016 to tackle this.
However, insufficient funding and high levels of non-participation by councils elsewhere in the country, are thought to be behind the low transfer rates.
London Councils is also concerned that a promised government funding boost will not be enough to cover the shortfall.
Besides an urgent £32m funding boost, the group is calling for government to support work by councils to develop viable improvements to the scheme.
Nickie Aiken, the group's executive member for schools and children's services, said: "London boroughs fear this will leave us unable to cope with caring for growing numbers of unaccompanied asylum seeking children.
"We urgently need additional funding and an open dialogue with government to get the National Transfer Scheme up and running again.
"If we cannot commit to supporting unaccompanied asylum seeking children properly, we risk putting them through a second ordeal."
Established in July 2016, the scheme was set up to relieve pressure on so-called "gateway" authorities, such as Kent and Hillingdon, that were having to care for large numbers of unaccompanied children entering the country via ports and airports.
Numbers of unaccompanied children aged under 18 increased by 17 per cent between 2016/17 and 2018/19.
There was also a near 50 per cent rise in formerly unaccompanied care leavers aged 18 to 25, according to data from a survey of 26 London boroughs.
According to London Councils, only about 60 per cent of the cost is covered by Home Office funding, a shortfall of more than £25,000 per child per year and does not include the costs of supporting unaccompanied children when they leave care.
In May, the government announced that councils will receive more funding for these children - £114 for each child every day that they are in their care and amounting to more than £41,600 per year per child.
The Home Office said it is committed to supporting a more balanced distribution of children across the UK.
It added: "We continue to work in partnership with the DfE and local government, including London Councils, to improve the scheme and call upon all authorities across the UK to step up and do their bit to support the care of these vulnerable children."