According to the new figures from housing charity Shelter, Yorkshire is facing a shortfall of thousands of properties with East Riding, Scarborough and York failing to provide even 10 per cent of the homes required.
The Government has abolished housing targets and promised to support the construction of affordable homes but already the housing quango the Homes and Communities Agency has seen 450m slashed from its budget and faces further cuts in the autumn.
Paul Landais-Stamp, York Council's housing strategy manager, said he is hopeful funds for 216 affordable properties will survive the cuts.
"Meeting affordable housing needs is going to be much more challenging under the new Government's budget restraints, and will be further affected by a continuation of the housing market recession given that over 80 per cent of new affordable housing is built as part of planning agreements on private developments.
"But, out of these challenges will come new ideas and initiative and the council will work tirelessly with its partners in the housing sector to explore new avenues of funding and new ways of meeting the pressing housing needs of York's residents."
A national commission will report its findings later this month and is expected to recommend radical changes.
A spokesman for Leeds City Council said the authority was trying to be "as inventive as possible", including the release of underused council assets to raise money for housing.
He said 413 affordable homes were delivered last year and it is confident a further 907 will be provided next year.
"We must face the fact that this money is now going to stop, so we need to find innovative ways to continue our work," he added. "However, we remain committed to providing the affordable housing the city needs."
The Government scrapped housing targets after regional spatial strategies were revoked.
Communities Secretary Eric Pickles said targets had failed to increase house-building and instead pledged to introduce financial incentives as a priority.
A spokesman for East Riding Council said the need for affordable housing had grown and the authority had secured the largest grant in the country – over 40m – for over 300 new affordable houses in the next 18 months.
"The impact of the recession has and will continue to have an impact on the prospects for the private sector delivering new affordable housing," he said.
"The council is keen to develop new ways of bringing forward affordable housing in areas where need is identified but the planning system needs to allow for a more flexible approach to delivering affordable housing."
Julian Rudd, head of housing at Ryedale Council, said the figure of 292 new affordable homes needed each year in Ryedale includes people with a mobility problems or those who live in a home in very poor state.
Grants and loans of more than 400,000 had been made to adapt or improve existing homes.
"These and many other initiatives help to address the vital issue of housing need. For Shelter to present the argument in this way is not at all reflective of the extensive efforts and results of Ryedale District Council and partners," he said.
Doncaster Council also disagreed with the figures, with a spokeswoman claiming it had an annual affordable housing requirement of 224, not 369.