It is hoped that proposed changes to responsible lending rules can help thousands of so-called mortgage prisoners secure a cheaper loan.
The Financial Conduct Authority (FCA) said its recent review of the mortgage market found that there were around 30,000 customers unable to switch and trapped by relatively high rates, despite being up-to-date with their existing
That is because they can no longer pass lenders' current affordability tests - barriers to irresponsible lending imposed after the financial crisis.
The FCA said a voluntary agreement would allow 10,000 customers of active lenders to switch to a cheaper deal.
But it said it would change how lenders assess whether or not a customer can afford the loan to help the other 20,000 borrowers who are with firms authorised to lend but are inactive.
It hoped the new proposals would also encourage 120,000 customers of unauthorised firms to consider whether they would benefit from switching.
The changes form part of its final report on the state of the mortgage market which found that, while it was generally working well, 30% of consumers could have saved cash in 2015/16 through seeking a cheaper deal.
It estimated around 800,000 paid a high reversion rate - the rate paid when an initial deal comes to an end - and did not
switch when they could.
The FCA's proposals include demands for the industry to use more innovative tools to help customers more easily identify what mortgages they qualify for and more help to find a mortgage broker.
Christopher Woolard, the FCA's executive director of strategy and competition, said: "The package of remedies we are taking forward will benefit consumers by encouraging innovation and making it easier for them to find the right
"We are particularly concerned about consumers - who are commonly referred to as mortgage prisoners - who are currently unable to switch.
"That is why we are acting now to help remove potential barriers in our rules.
"These changes should make it easier for consumers to get a more affordable mortgage."
The proposals were welcomed by campaigners at MoneySavingExpert.com
Its founder, Martin Lewis, said: "The absurd current rules have meant existing mortgage customers who are just trying to switch to a new deal have been flabbergasted to be told 'you can't afford a cheaper mortgage.'
"That risks people defaulting and ultimately being repossessed, and for many, effectively means the remortgage market is broken.
"I strongly support affordability tests for first-time buyers - we don't want people getting into debt that they can't afford to repay.
"This involves stress tests to see not only if they can afford the mortgage, but if they could do so if interest rates rose to 6% or 7%.
"Yet to use that same test for those that are remortgaging without moving house, without borrowing more and without change of circumstance, is nonsensical."