According to research from Yorkshire Building Society, which collected data from 1,000 adults, this figure rises to more than 60% in those aged over 55 who own their own homes.
The government-backed scheme would have support with information, moving, costs and logistics.
The report added that the desire to downsize was greatest among Londoners, at 68%.
Only 45% of women said they would take up the offer to downsize, compared to 54% of men.
However, around 45% of potential downsizers said the lack of suitable homes is the main reason for them staying put.
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Around two-thirds of over-55s said a lack of understanding was a key issue, and cost was also highlighted as a potential barrier.
Ben Merritt, director of mortgages at Yorkshire Building Society, said: “Downsizing is an often-overlooked element of the housing market but is vital to freeing up homes for those further down the housing chain.
“Longer-term homeowners are telling us they have a desire to move to something smaller but it’s not possible due to the cost and the fact there is nowhere suitable for them to go and a lack of support to guide them through the process. That’s a problem the industry needs to collectively resolve.
“The stamp duty changes [that] came into force on 1 April will make it more, not less, expensive to move, so these latest findings underline our calls for a strategic review of the housing market, overseen by an independent commission.
“While suggestions that the government is looking at a potential review of this and other property-related taxes are potentially positive, it will be important to consider the needs of people at all stages of the housing cycle and avoid the potential for unintended consequences.”
Merritt added: “Clearly, a significant proportion of UK homeowners have the equity, motivation and a clear desire to downsize — but the system isn’t set up to help them do it.
“Government and industry now need to unite behind changing that to free this property log jam for the good of people at all stages of the homeownership journey, not least the first-time buyers, who are essential to whole housing chains.”
