The UK has built more than a million fewer houses since 2004 than are needed to keep up with demand, according to analysis.
Yorkshire Building Society analysed government figures showing how many homes have been built since 2004, when a report highlighted how England needed to revamp its housing supply.
It pointed to the Barker Review of Housing Supply, which suggested that 270,000 houses were needed a year in England alone to bring house price inflation under control.
The Yorkshire found the number of housing completions across the UK has never reached the 270,000 level - and it said at least 1.2 million additional homes would be needed.
Andrew McPhillips, chief economist at Yorkshire Building Society, said: "The Brexit decision and the uncertainty it creates around the prospects for private sector house builders, not to mention the country's economic outlook, is likely to heighten the housing crisis.
"Addressing the shortage of homes must remain high on the Government's agenda regardless of the work required following the EU vote.
"We need a clear strategy to deliver the 1.2 million additional homes and options like giving local councils fuller control of existing housing funding, as well as freedom to develop surplus public land, should form a key part of that.
"The longer we leave the supply crisis to worsen, the more difficult it will be to resolve. The UK has failed to build the number of homes needed to meet demand year after year, which has consequently inflated prices and made it even more difficult for those looking to buy."
A Department for Communities and Local Government (DCLG) spokeswoman said: "We've got the country building again - with the numbers of new homes increased by 25% in the last year alone.
"The Government has set out the most ambitious vision for housing in a generation, doubling the housing budget to deliver on its ambition to build a million new homes."