A letter signed by 14 council leaders to Home Secretary Sajid Javid, seen by The Yorkshire Post, says there is a risk of “catastrophic failure” for the system which provides accommodation for those seeking refugee status.
Local councils say they are being increasingly side-lined and that many towns and cities across the North each have more asylum seekers “clustered in a handful of wards than entire regions in the South and East of the country”.
The future of the £600m contract to provide asylum housing in Yorkshire between 2019 and 2029 was thrown into doubt this summer after it emerged that there were no successful bids to run it when it comes up for renewal next September.
It is understood that a bid by outsourcing giant G4S, which has been suffering financial losses while running the service since 2012 due to having to deal with more asylum seekers than expected, was not accepted by the Home Office.
New bidders are now being sought for the ten-year contract, leading to fears that local authorities may have to accept higher numbers of asylum seekers and poorer quality accommodation so the Government can persuade a company to run the scheme.
North Yorkshire council leaders, who had been in the process of agreeing to accept asylum seekers for the first time, have now halted negotiations until they get assurances from the Government.
And some of the ten Yorkshire authorities who are taking part say they are now giving “serious consideration” to pulling out.
According to the leaders, which represent Labour and Tory-run administrations, the “mounting chaos” now surrounding the system is leading to a significant risk of a housing crisis for asylum seekers in Yorkshire from next year.
They fear a repeat of 2012, when G4S were unable to find enough homes in Yorkshire and councils were forced to step in to avoid possible “mass sudden homelessness of hundreds of asylum seekers”.
In the letter to Mr Javid they call on him to “personally intervene to enable the Home Office to get a grip on the asylum system and enable them to work in partnership with, rather than exclude, local authorities”.
It says: "For too long, asylum dispersal has been implemented as something done to local authorities and communities in the North of England rather than done with them in partnership, with little heed paid to concerns raised about cohesion or disproportionate concentrations of asylum seekers in our towns and cities.
"A number of local authorities have regularly expressed these immigration concerns to the Home Office and Immigration Ministers, but we have experienced little urgency in addressing them."
It added: "Being an asylum dispersal area is voluntary and some local authorities in our region have over recent months been giving serious consideration to actively pursuing withdrawal.
"The current process of procurement for the new asylum system is making this outcome increasingly likely, whilst for potential new areas there is reduced incentive to join.
"We fear that the Home Office continuing the current approach risks catastrophic failure of the new asylum system as soon as it begins."
Of the 5,054 asylum seekers homes in Yorkshire and the Humber between January and March, the latest period for which data is available, the majority were in the region's biggest cities Leeds, Bradford, Sheffield and Hull.
Some 793 were housed in Bradford alone, but there were none in York, Craven, Hambleton, North Lincolnshire, Richmondshire, Ryedale, Scarborough, Selby, Harrogate and the East Riding of Yorkshire.
A Home Office spokeswoman said: “There is an ongoing procurement process for the asylum accommodation and support contract for the North East, Yorkshire and Humber region.
“We are confident of having a fully operational contract before the expiry of the current contract, with sufficient time to properly transition the services.”
G4S declined to comment.