In a letter to the Guardian, Cllr David Hodge – leader of the Tories at the Local Government Association (LGA) – warns that elements of the bill being debated in the Lords this week could have the “unintended consequence of increasing homelessness and pushing more families into the more expensive private rented sector”.

Hodge has teamed up with his Labour and Liberal Democrat counterparts to ask members of the House of Lords to try to block legislation that would force councils to sell their most expensive properties in order to fund the government’s Right to Buy policy.

“At a minimum, we urge peers to back amendments that allow councils to retain enough receipts from every home sold to be able to replace it in the same area,” they write.

They have also raised concerns about the government’s starter homes scheme, which means that one in five properties in new developments will be available to first-time buyers under 40 at a 20% discount.

Critics say that only middle or higher income earners could qualify for those homes, and yet developers will be able to classify them as “affordable”.

“Current proposals for starter homes carry a risk that a crucial supply of new affordable rented homes will be displaced, and despite 20% discounts they will still be out of reach for the majority of people in need of an affordable home,” write the local government leaders.

A number of the amendments have been laid down by LGA president and former head of the civil service, Lord Kerslake. “The amendments are trying to do three things,” he said. “To make it a fairer bill, so that it is not transferring resources from social housing for rent to ownership. To make it more localist. And to make it more workable. The numbers do not add up.”

The peer said he wasn’t against ownership but argued that for many people it was simply out of reach.

But the housing minister, Brandon Lewis, said the policies were intended to help people realise their ambition to own a home. He told the Guardian that 86% of people still aspired to homeownership.

“The hardest hit part of the housing market was first-time buyers and we are very clear that we want to increase supply but also ownership,” said Lewis, who argued that a 20% discount on an average property did make it much more affordable for ordinary people. He also argued that councils could still push for developments to include other forms of affordable homes on top of the government’s new scheme.

Those against the plans believe that starter homes are out of reach for the poorest. Campbell Robb, Shelter’s chief executive, said: “By building homes for people on middle to high incomes, the government is redistributing existing resources away from those on low incomes. This will have a massive impact on ordinary families being priced out of the dream of owning their own home, and millennials faced with expensive and unstable private renting, or living with their parents well into their 30s.”