The Local Government Association (LGA) has urged peers to rewrite major elements of the Government's controversial shake-up of housing policy.
Tory David Hodge and the leaders of the Labour, Liberal Democrat and independent groups on the LGA, warned that ministers' plans could increase homelessness.
The legislation includes extending the right to buy to housing association tenants and the building of 200,000 "starter homes", have cleared the Commons.
But the senior councillors raised concerns about the plans which would see local authorities forced to sell off vacant high-value council houses in order to subsidise the extension of right to buy.
In a letter to The Guardian, Mr Hodge and his cross-party allies urged peers to back amendments to the Housing and Planning Bill "that we believe are vital to giving councils and the Government a better chance of solving our housing crisis".
They said: "We support the Bill's intention to build more homes but are concerned that some proposals run the risk of reducing the number of genuinely affordable rented homes that our local communities desperately need.
"Proposals forcing councils to make payments to Government based on selling council homes will hamper councils' abilities to invest in new affordable council housing and is likely to have the unintended consequence of increasing homelessness and pushing more families into the more expensive private rented sector."
The legislation is being debated on Monday and the senior councillors said: "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.
"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.
"Councils support measures to boost home ownership and starter homes are one of the ways this can be achieved, but we are also urging peers to back amendments allowing councils to decide how many starter homes, alongside affordable rented homes, are on each development to ensure they meet the needs identified by councils with their communities."
Meanwhile, Labour highlighted figures showing less than a quarter of under-35s in England will own their home by 2020, claiming it was the result of the "complete failure" of the Government's housing policies.
The Labour analysis of English Housing Survey data show there were 1.6 million under-35 homeowners in 2009-10, some 40%, but by 2020 the figure is expected to be 991,000 or 24%.
Shadow housing minister John Healey said owning a home was not becoming a "luxury" for those on the highest salaries or whose parents could afford to help.
Mr Healey and Labour leader Jeremy Corbyn are set to make tackling the housing crisis a key part of their local election campaign ahead of the May 5 ballot.
"We need more good homes of all types to fix the country's housing crisis," Mr Healey said.
"The shocking fall in home-ownership over the last six years shows that what used to be a natural part of growing up is becoming a luxury for those on the highest salaries, or whose parents have the deepest pockets.
"A million more families became home-owners under Labour but on the Tories' watch the number of young people owning a home is now in freefall.
"This is a complete failure. Ministers have got no long-term plan for declining home-ownership and a worsening housing crisis."
In response to the LGA's letter Housing Minister Brandon Lewis said: "This Government is determined to help anyone who aspires to own their own home achieve their dream.
"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.
"We are doing this with the biggest house building programme since the 1970s which includes delivering on our manifesto mandate to introduce starter homes at a 20% discount and delivering the homes our country needs."