A cross-party group of MPs on the Public Accounts Committee has blasted government's plan to extend the Right to Buy to housing association tenants and said it should be "embarrassed" by the policy's lack of detail. The government said more information would be released soon.

Under the Housing and Planning Bill, which is still before parliament, housing associations will be able to take part in the Right to Buy scheme for their tenants. The extension will be offset through the sale of high-value empty council homes.

Currently, Right to Buy only exists for council tenants. Introduced by the Thatcher government, which pledged to create a property-owning democracy, it offers council tenants the opportunity to buy their homes at a discount.

The PAC said the government has so far failed to provide a detailed impact assessment on the policy, which critics say will deplete the social housing stock. The committee also notes the absence of specific costings on exactly how it will be funded or what the financial risks are. The report also said the government should commit to replacing homes sold on at least one-for-one and on a like-for-like basis, so the quality of housing is not affected. The government should also address the risk of fraud, said MPs.

"The government should be embarrassed by the findings of this report," said Meg Hillier, chair of the PAC. "Extending Right to Buy will affect many thousands of people, yet the department has failed to provide basic information to support its stated aims. Instead we have heard vague assertions about what it will accomplish and how.

"The approach to paying for this policy seems to be entirely speculative. On the basis of evidence heard by our Committee, there are no costings or workings out. We are not talking about a 'back of an envelope' calculation — there is no envelope at all. The department has not made a diligent and credible case for this policy."

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But a spokesman for the Department for Communities and Local Government (DCLG) said it was planning to release more information about the policy, which has not yet become law.

"This government is delivering on its commitment to give more people the chance to become homeowners," he said. "Our voluntary agreement with housing associations will mean 1.3 million tenants will have the chance to own their own home while every home sold will be replaced with a new affordable property. And for each higher value home sold off, it will be replaced with a new affordable property on a one-for-one basis – and two-for-one in London.

"We are currently working jointly with the housing association sector to deliver on this promise, and are running a pilot to assess how the scheme is working in practice to help the first tenants to buy their homes. We have always been clear we will set out further information as part of this process and regulations defining higher value will be subject to parliamentary scrutiny."

John Healey, Labour's shadow housing minister, said the "mass forced sale of council homes to pay for new Right to Buy discounts will mean the loss of thousands of affordable homes at a time when they have never been needed more".

"Parliament should not be asked to accept this part of the Housing and Planning Bill, without MPs and peers knowing what they are voting for," he said. "Ministers must now pause this part of the legislation until they are able to give Parliament some answers."

The government suffered a number of defeats on its controversial housing bill in the House of Lords, losing votes on amendments watering down several key parts of the legislation, which is intended to increase home ownership and housebuilding. It now faces compromising on the original bill or delaying its passage into law.