Councils had also “lost confidence” in central government for failing to listen to their concerns over the quality of some accommodation, the home affairs committee said.
“The cost of asylum accommodation does not end with housing provision,” the committee said, in its report released on Monday.
“Local authorities must also provide public services, such as safeguarding and education, and manage the effect on the wider community.”
The MPs added: “This additional requirement has been felt most acutely by the small number of councils that have a disproportionately large amount of asylum accommodation in their areas.”
The report comes as the government is preparing for the last round of tendering to replace the asylum accommodation Commercial and Operational Managers Procuring Asylum Support Services (COMPASS) contracts – worth £4bn over 10 years – currently delivered by companies G4S, Serco and Clearsprings. The contracts will be replaced next year.
Councils – that used to hold the contracts for housing asylum seekers – can sign up to the voluntary ‘dispersal’ scheme to house asylum seekers in their areas.
The committee warned of “significant risks to asylum accommodation provision if the government doesn't urgently engage with local authorities who are considering withdrawing from the dispersal scheme due to the government's handling of the replacement for the current contract”.
“Local authorities have a clear interest in the way that the future asylum accommodation contracts are managed but have been largely excluded from the process of developing the new contracts,” the report said.
“More equitable treatment must be given to authorities that participate in the dispersal system, and adequate support must be provided to mitigate unfunded cost pressures.”
The report also found “very little improvement” in the quality of asylum accommodation since its last report on the topic two years ago. The committee said that vulnerable people were being housed in badly maintained, damp and vermin infested properties.
“Glasgow, Manchester, Wolverhampton and communities across the UK have done so much to support those seeking asylum in the UK. Yet, the government has done little to support them, Stuart McDonald, member of the committee, said
“Local authorities have lost confidence in the system because the government has failed to listen and respond to their concerns.”
The committee report said: “In the final weeks before contracts for asylum accommodation worth billions of pounds are agreed, the government must ensure they provide for a long-term, workable partnership with local authorities.
“The local authorities who step up and continue the UK's proud tradition of providing asylum must not be placed at a financial disadvantage because of it.”
It also suggested responsibility was shared more widely, and distributed between more authorities, to correct the “unfairness” of the current arrangements.
A Home Office spokesperson said: “We monitor contractors and their accommodation closely and take action – including financial penalties – where issues are not addressed within certain timescales.
“We continue to work closely with local authorities on asylum dispersal and have committed to comprehensive engagement with the Local Government Association and local authority chief executives to review the process.”