Crawley Borough Council fears it could face bankruptcy if thousands of Chagos islanders choose to settle in its area.
Chagossians were forced to leave their homeland when Britain bought the islands in the Indian Ocean in the 1960s, with many settling in Crawley.
More people of Chagossian descent are now eligible for British passports but Crawley Borough Council fears providing housing for them would be unaffordable.
The Home Office said the government was looking at supporting councils.
With a community of 3,000 Chagossians already settled in Crawley, the council said between 3,000 and 5,000 more could claim British citizenship, with many choosing to join their relatives in West Sussex.
The application process for people of Chagossian descent to secure British nationality opened in November.
In a joint letter to the government, written with West Sussex County Council, Crawley Borough Council said the extra costs of housing more Chagossians could result in it declaring a section 114 notice, effectively declaring bankruptcy.
Crawley Borough Council said the sums involved in providing services to islanders moving to the town would be beyond the means of even the largest local authorities.
Councillor Michael Jones, leader of Crawley Borough Council, said: “I do not think it is either unfair or hyperbole to describe this as a crisis situation for Crawley.
“As a town, we are already facing historically-high housing pressures, with temporary accommodation units approaching 350 and becoming a significant budget pressure for the council, and a housing waiting list of around 2,000.”
The letter claims that 100 households arriving in Crawley without housing would cost £227,500 every month in temporary accommodation costs, but if the number rose to 2,000 it would cost the authority £4.5m a month.
The Chagos Islands is an archipelago formed of more than 60 islands in the Indian Ocean.
The islands were historically part of Mauritius, which had been a British colony since 1814. They sold the islands to the UK for £3m in 1965.
The UK evicted Chagossians from the archipelago between 1967 and 1973 so that the US could erect a military base on Diego Garcia, the largest island in the group.
Many of those exiled were resettled in Crawley. The decision to allow more Chagossians British citizenship has been welcomed by Chagossians in Crawley.
Mylene Agustin runs a lunch club for islanders in the town, and said:
“It’s good news. My niece who lives in Mauritius can finally join me here.
“I just want the government to support those who arrive as I don’t want them to face the same trauma as my parents who were exiled from the Chagos islands in the 1960s.”
Another club regular, Frankie Bontemp, said: “The main issue has not been addressed for the right of return and the on-going negotiations between the UK and Mauritius where Chagossians have been excluded so far.”
A Home Office spokesperson said: “On 23 November 2022 we opened a bespoke route allowing Chagossian descendants to apply for British citizenship free of charge.
“This new route gives anyone of Chagossian descent the security to plan for their future as a British citizen and the certainty this brings.
“We are working across government, with local councils and local authorities to understand what support is needed for Chagossian descendants who decide to come to the UK through this new route.”
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