Councils in the benefit cap pilot say the money given by the Department of Work and Pensions to introduce the scheme is not enough.
Councils in London have been the first to test out the benefit cap being placed on welfare benefits, and find the suggest amount leaves them out of pocket.
The pilot that has started with four councils is designed to test the changes made to welfare benefits before it is rolled out nationally.
Couples and lone parents will not receive more than £500 a week while a £350 limit applies to single people. This will include jobseeker's allowance, income support, child and housing benefit.
Critics have said the cap failed to tackle underlying issues, like the cost of housing and regional differences
The pilot started on Monday, and already they have found that they have not received enough money to implement the changes.
Enfield, Croydon, Haringey and Bromley councils have implemented the £26,000-a-year benefit cap. The councils must identify who is eligible for the cap and administer the new system.
The Department for Work and Pensions provided £2 million to help the four councils cover implementation costs, such as extra staff, administration, IT work and meeting any shortfall in housing benefit in the short term. The councils have also been allocated a senior Jobcentre manager to help people find work who are affected by the cap.
However, the first four local authorities to test the government's new benefit cap have warned they have not received enough money to implement the changes, which would leave the councils at a loss on an already tightened budget.
Haringey Council received £115,350 from the DWP, but has calculated that costs will be £220,000 more.
Croydon Council, received just under £500,000, but felt it had not been given the funds it needed. A council spokesperson added:
We have had assurances from [Lord David Freud] that he will look at these issues as a matter of priority.
A spokesperson from Enfield Council, which received £815,000, said:
It's difficult to know the scale of homelessness it may cause, in which case it might cost us a lot more.
Every other council in England will implement the cap from July, but Sir Steve Bullock, executive member for housing at umbrella body London Councils, said the impact of the trial will not be established as there will be no analysis of the pilot before being introduced nationally.
A DWP spokesperson said the department was working closely with the four councils to ensure they were given the right level of support.