The supply of houses for sale in Britain is at its lowest level since the 1970s, according to Nationwide.
Unless more houses are built, there is a danger that the supply will continue to dwindle and this would push up house prices yet more, it warned.
Currently, the average house price in the UK is £196,305, according to the lender.
Nationwide urged policymakers to build hundreds of thousands of new dwellings to meet growing demand.
"Only 135,000 new homes were built in England in the 12 months to September 2015, well below the approximate 220,000 new households that are projected to form each year over the next decade,” said Robert Gardner, Nationwide's chief economist.
The current rate of construction is “well below” what is needed to accommodate population growth, he said.
The Chancellor doubled the Government’s housing budget this week to £2 billion a year. He said he would find funding to build 400,000 new homes in England by 2020.
The policy was part of a “bold plan to back families who aspire to buy their own home”, he said. Half the homes would be for first-time buyers and sold at 80% of their market value.
Land Registry data showed completed house sales in England and Wales fell by 15% to 74,596 in August this year. The number in August 2014 was 87,895.
The number of houses sold for over £1 million also went down 13% to 1,280 from 1,473 the year before, following the stamp duty leap to 12% for properties valued at more than £1 million.
