The regulations, outlined in the Budget, would restrict housing benefit for rents which exceed an average local 'reference rent', with the council paying half the excess.
Under the changes local authorities will have a limited fund from which to pay discretionary excess rents for vulnerable tenants.
John Perry of the CIH warned there are not enough trained officers to cope with 'the significant increase in discretionary decisions under the new system'.
HAMA schemes, with rents at market prices to cover running costs and provide incentives for private landlords, will be under-represented in the calculations for average council rents.
The CIH suggested that HAMAs be excluded from the new regulations, which are being reviewed by the Social Security Advisory Committee and will go through Parliament in June.