But economic secretary MP John Glen and Mr Bailey both wrote to Treasury select committee chairwoman Nicky Morgan, stating it would be the decision of the lender whether it chose to use the new affordability rules for anyone seeking to remortgage as it was a "commercial decision".
The City-watchdog also proposed that inactive lenders and administrators acting for unregulated firms should review their customer books to identify eligible consumers and highlight the rule changes to them — but would have 13 months to contact them.
Mr Bailey said that he hoped the proposed changes to mortgage rules would be in place before the end of the year.
The plight of mortgage prisoners has hit the headlines recently as pressure group UK Mortgage Prisoners put pressure on the Treasury and the FCA and MPs rallied their support for such consumers in a cross-party group.
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