Halifax's "generation rent" report found that despite schemes such as Help to Buy giving a boost to people with small deposits, the proportion of 20 to 45-year-olds with realistic prospect of owning their home in the next five years has remained broadly unchanged from previous years, at 36%.
Almost one in five (18%) people aged 23 to 27 said they have no desire to own their own home.
The report warned any future collapse in the number of first-time buyers - seen as the "life blood" of the housing market - will have an impact on people trying to move up the property ladder, and could bring the market to a "standstill".
The findings come after figures released by the Office for National Statistics (ONS) earlier this week showed someone trying to get on the property ladder faces paying 10.5% more for a home than a year ago, with the typical price paid by first-time buyers reaching £192,000 in February.
The ONS figures have fuelled concerns about "runaway train" house prices, with property values across the UK having leapt by 9.1% over the last year to a new average high of £253,000. In Scotland, prices rose 2.4% to an average of £183,000.
The Halifax report found almost half (48%) of people agree Britain will become a nation of renters within the next generation and 46% think it is becoming more like other parts of Europe, where long-term renting is seen as the norm.
On average, people who do not own a home said they would be prepared to save for a deposit to buy a home for around five-and-a-quarter years, down from nearly five-and-a-half years on last year.
About three in 10 people aged between 20 and 45 think Government housing market initiatives are working, according to the findings, but the same proportion believe they are not and the remaining four in 10 do not know.
Some experts have said the Help to Buy scheme is partly to blame for house prices being pushed towards unaffordable levels. The scheme, which fully launched last year, is designed to help people with a deposit as low as 5% get on to or up the property ladder.
The Government has said a series of initiatives is helping to boost the supply of homes for potential buyers to choose from.
Toughened mortgage lending rules are also set to come in later this month, which will see applicants being asked more probing questions about their spending.
The report also showed a heavy reliance on the "bank of mum and dad", with six in 10 aged 20 to 45 agreeing support from family is now assumed as vital in helping people on to the property ladder.
Craig McKinlay, mortgages director at Halifax, said: "We may be heading towards the point where the aspiration to own a nice home will be replaced by the aspiration to simply live in one. It seems people are now beginning to accept a lifetime of renting."