Young people will find it harder to get on the housing ladder if the UK stays in the EU, Leave campaigner and former Tory minister Liam Fox says.
In an appeal to younger voters, he said immigration puts pressure on housing stock, increasing rent costs and competition to buy homes.
Further "uncontrolled migration" will make it "harder to get a home of your own", Mr Fox added.
The Remain campaign dismissed his argument as a "fantasy".
The Leave campaign has stepped up its focus on immigration in recent days, with just over three weeks to go until the referendum on 23 June.
In a speech from Vote Leave's headquarters, Mr Fox targeted younger voters with a warning about the impact on housing of "uncontrolled migration" from the EU.
He will say: "Most new immigrants move into the private rented sector which has grown as the immigrant population has grown.
"Competition for rented accommodation obliges all those in the private rented sector to pay high rents which take a large share of income and makes saving to buy a home even harder.
"These resulting high rents and a shortage of housing make it much more difficult for young people to set up home on their own so they have to spend more time in house shares or with their parents."
The former defence minister warned there was no "realistic possibility" that money would be found to fund the extra infrastructure needed to match migration levels if the UK voted to stay in the EU.
He also warned that migration pressures would have a negative impact on the green belt with "more of our open spaces and natural greenery being turned over to housing".
"If we remain in the EU, if we have uncontrolled migration year after year after year after year, you will find it harder to get a home of your own.
"You will find it harder to see a GP or you will find it harder to get a school place and you will see our green spaces disappear at an even greater rate," he added.
Liberal Democrat Tim Farron attacked Mr Fox's argument, arguing that leaving the EU would "destroy young people's hopes of getting on the housing ladder".
"Leaving would mean fewer jobs, higher prices and lower pay, making deposits harder or impossible to build up. And it means higher mortgage payments making first time loans less affordable.
"First time buyers are better off in Europe and leaving would be a leap in the dark leaving young people worse off," the Remain campaigner added.
House builders also criticised Mr Fox's argument - saying the construction of new homes would stall if Britain left the EU.
James Hopkins, executive chairman of Hopkins Homes, said: "My greatest fear is that leaving the EU will exacerbate the housing crisis, bringing economic uncertainty and with it stagnation in the housing market.
"Instead of moving from 'Generation rent' to 'Generation buy' we could move to 'Generation debt'."
Meanwhile, Philip Makepeace, managing director of Norfolk Homes, said economists' predictions of a recession following a vote to leave would damage the UK house building industry.