The Association of London Government wrote to Mr Straw last week seeking an urgent meeting to lobby for similar guarantees provided to Kent CC earlier this month. Mr Straw has agreed to meet the association but no date has been fixed.
The letter said: 'Boroughs cannot offer the leadership needed if resources for other essential services are drained. London, like Kent, is full.'
Kent has been assured that refugees arriving at its ports will be fast-tracked through the National Asylum Support Service and moved away from the county.
It is also seeking funds to cover the costs incurred in 1999-2000 and a commitment to pay the full cost of providing services to asylum seekers this year. The association puts the annual shortfall for London boroughs at£30m.