Hillingdon Council has raised concerns over the financial impact of recent arrivals from the Chagos Islands.
Since July, 621 Chagossian individuals have flown into Heathrow, with 157 more expected this week.
While the Government covers support for the first 10 days, the council must provide assistance beyond that period. Hillingdon estimates the extra demand could cost around £2m by the end of the year.
Cllr Steve Tuckwell, cabinet member for Planning, Housing and Growth, said local residents were effectively footing the bill.
‘Our officers are stretched, essential services are under immense pressure, and still the Government expects local councils to cope without adequate support. This is unsustainable,’ he said.
‘The Government must act now and fully fund the costs associated with its own policies and stop laying the responsibility at the door of Hillingdon residents.’
The London borough's plea follows similar warnings from the Greater Manchester Combined Authority and Crawley Borough Council.