According to a study by the HomeOwners Alliance (HOA), 73% of non-homeowners desire to own their own property, up from 65% four years ago.
However, 78% say the availability of housing is a "serious problem".
In addition, one in two (52%) of adults say quality of housing is also an issue, up from 49% last year.
The HOA said London is a "hotspot" for housing concerns. The capital registers higher levels of concern than the UK overall for house prices, availability and quality of housing, ability to get a mortgage/ remortgage, stamp duty rates, gazumping and leasehold / freehold system.
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Concern about house prices, availability and quality of homes are also rising over time.
However, the North West and Scotland are more positive housing markets generally.
The North West registers lower levels of concern in areas such as house prices, availability, and quality of housing, as well as, ability to save for a deposit, get a mortgage/ remortgage, repay a mortgage, move up the housing ladder, homebuying/ selling process and property solicitor/ conveyancing fees.
In Scotland, house prices, the quality of housing and saving for a deposit are less of a concern than in the UK overall, while issues relating to the homebuying / selling process and stamp duty rates are also seen to be less serious problems.
Paula Higgins, the Chief Executive of the HOA, said: "Despite a blizzard of government initiatives aimed at helping homeowners, the housing crisis is deepening across the country, with ever more non-homeowners wanting their own home, and ever greater concern about the lack of housing.
"Many government policies have boosted demand for homes, but what this survey shows is that the real problem is the desperate shortage of houses. Until the government tackles the fundamental issue that we just don’t have enough good quality homes, the housing crisis will continue to deepen and a generation will continue to have their dreams of homeownership crushed."
(LM)
