Hounslow Council had to pick up a £750,000 bill last year because of a shortfall in funding for young asylum seekers living in the borough.
Government ministers have agreed to look into a Civic Centre claim for extra money each year to pay for the care of vulnerable unaccompanied asylum seeking children (UASC).
Cllr Paul Lynch, executive member for education and children at Hounslow Council, said: "We have a duty of care to every young person in the borough and Government legislation requires us to provide a range of services to them.
"But legislation governing the care that should be provided to them conflicts with the Government's own rules about the grants councils can be paid to provide such services.
"Last year alone in Hounslow we had a short-fall of almost three quarters of a million pounds. We need a long-term solution that refunds 100 per cent of the costs to local authorities. Leaving this bill unmet makes it continually more difficult to provide appropriate care for these vulnerable children and can create resentment in our communities."
The new review follows a recent meeting at the House of Lords where Hounslow was among 10 local authorities who met with Ministers, Government officials, refugee and children's charities, MPs, and Peers to discuss the challenges of supporting thousands of UASC.
Last year the shortfall in funding for UASC living in Hounslow was £740,000.