First-time buyers will find it harder to get on the property ladder if Britain votes to leave the EU, a group of 17 of the UK’s biggest housebuilders has claimed.

The group, including Barratt Homes, Berkeley Group and housing associations such as Peabody, said in an open letter that Brexit would put the dream of home ownership at risk.

It comes just weeks after a Treasury report also suggested house prices could crash by up to 17% in the event of Britain leaving the EU.

However, the leave campaign claims this is a poor argument for remaining in the EU, with first-time buyers and their parents not averse to the idea of the housing market cooling down.

But in a coordinated announcement, the housebuilders said it would be harder and more expensive to build homes in the event of leaving the EU.

They said that a vote to leave would create “considerable uncertainty for Britain”, meaning that “investment will suffer as confidence in the economy wavers”, making it harder for housebuilders to raise the funds to undertake new development.

They also argue that the supply chain, which they say employs millions of people across the UK, would be damaged, with a vote to leave disrupting the production and import of materials such as bricks.

They conclude that leaving the EU would be a risk and therefore they support Britain remaining in the EU.

The 17 firms – Metropolitan, Notting Hill Housing, Canary Wharf Group, the Larkfleet Group, A2Dominion Group, Family Mosaic, Peabody, Genesis Housing Association, the Berkeley Group, Barratt Developments, Norfolk Homes, Crest Nicholson, Hopkins Homes, L&Q, Pocket Living, Cast, and Wates Group – employ more than 34,000 people.

Ruth Davidson, leader of the Scottish Conservative party, said it was clear the “fantasy economics of the leave campaign would put this universal dream at risk”.

The leave campaign has repeatedly argued that young people wanting to buy a house for the first time would benefit from Brexit.

Last month, Chris Grayling, the leader of the House of Commons and a leave campaigner, said staying in the EU would make it more difficult for young people to get a foothold on the housing ladder or find affordable rents because the government would be unable to control European immigration. He told the Guardian that younger voters must consider the “practical consequences” of a vote to remain in the EU and said that rising house prices were partly caused by migration into the UK.

His comments triggered an angry reaction from remain campaigners, who accused him of reaching for the “Farage playbook”.