An Ipsos Mori index for August showed housing was cited as a concern by 22% of people, up 6 points from July, reaching its highest recorded score on the index since October 1974.
Housing was a particular concern among younger people where one in four 18-34 year olds mentioned it compared with 17% of those aged 55+, the research found.
Greater London also emerged as a hotspot for housing concerns after 44% of its residents mentioned the worry.
The UK has been chronically short of affordable housing stock, with MPs predicting a crisis if the market does not change.
Figures released by the Department for Communities and Local Government in August showed the number of new houses brought to market in England between April and June had risen 7% on the previous quarter, with both the private sector and housing associations reporting an increase.
However, industry said the “modest” rate was not enough to reach government targets of building one million new homes by 2020, which needed market reform.
Ipso’s Mori found renters were more likely to mention housing as a concern than those either paying a mortgage or who own their home outright.
The firm’s monthly data provides an overview of the key issues concerning the country. It interviewed a representative quota sample of 1,025 adults aged 18+ across the UK in the first two weeks of August.
Overall housing came fifth in the list of current concerns, falling just behind the economy, NHS, the EU and the number one, immigration.
Immigration once again took the top spot with one in three saying it was their concern (down four points from July) despite being at its lowest level since March 2015, Ipsos Mori said.
The survey found Britain’s decision to leave the EU remained the single most important issue facing Britons after it was mentioned by 21% as their biggest fear.
However, the concern had dropped nine points since July, when it reached record levels, to three in ten adults now saying they are concerned about the EU.