The City regulator is planning a change of rules that could lower the housing costs of thousands of so-called "mortgage prisoners".
Some 140,000 homeowners are trapped on high interest-rate home loans with unregulated or inactive firms, and are unable to switch to a cheaper deal.
The Financial Conduct Authority (FCA) has now said it is considering a change to its affordability checks.
This could allow these people to switch to deals that are easier to pay.
At present, they are stuck on high default rates, owing to an FCA requirement - introduced in 2014 - for mortgage holders to meet strict affordability criteria when they apply for a new fixed deal.
In a letter to the Treasury Committee of MPs, FCA chief executive Andrew Bailey said the planned changes would apply only to those in this situation who are not seeking to borrow more on their mortgage, but just want to get the cost down.
"The test would be whether the new mortgage costs are more affordable than the current mortgage costs," he said.
Banks and building societies would still need to agree to take on these customers.
Jackie Bennett, director of mortgages at UK Finance, which represents banks, said: "We will continue to work constructively with our broad range of members and the FCA to help ensure those customers who want a like-for-like mortgage can switch lenders more easily."
Northern Rock fallout
An interim report into the mortgage market, published in May by the FCA, highlighted the plight of these borrowers.
These "mortgage prisoners" are unable to move to a better deal when their existing mortgages switched to the more expensive standard variable rate, even if they could meet the payments.
The FCA said it had identified about 150,000 such customers.
Of these, about 30,000 were with authorised mortgage lenders, while about 120,000 had mortgages held by non-regulated firms, which include some previous Northern Rock and Bradford & Bingley customers.
Some are saddled with such high costs that they face the prospect of falling behind on repayments.
Some 10,000 of them are with lenders who are still actively operating in the mortgage market. These customers have received letters during the latter half of last year outlining some of the alternative mortgage deals available from their existing lender.
The new proposals flagged by the FCA would change the regulations to assist the rest.
Nicky Morgan, who chairs the Treasury Committee, said: "The regulator must now act swiftly to help these 140,000 mortgage prisoners and not use this consultation to kick the issue into the long grass."
Martin Lewis, founder of MoneySavingExpert, who has campaigned on the issue, said: "Finally, a welcome and sensible move. For over four years we've been saying that it's ludicrous that people are failing affordability tests because they're absurdly told they cannot afford a cheaper deal than the one they're already on."
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