Consumer groups today urged watchdogs not to let banks off the hook over payment protection insurance mis-selling after the Financial Services Authority said it would consider imposing a deadline for claims.

Banks have been lobbying hard for a time limit on compensation claims, which have cost more than £10bn and could end up at double that amount.The British Bankers' Association has called for a cut-off date to be set at May 2014. But the Financial Services Authority said that it would only act if it believed such a move would be in the consumers' interest, and that it could only be imposed after extensive consultations and a massive ad campaign.

"Our key priority is to ensure consumers are protected, so the FSA board would need to be convinced that any proposals would be in the interests of consumers," it said.

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Consumer groups last night hit out at the BBA proposal, arguing that claims were already time limited. Under current rules they have to be lodged within six years of a PPI policy being bought or within three years of a claimant becoming aware that their policy was mis-sold.

Peter Vicary-Smith, chief executive of Which?, said: "It's in everyone's interest to draw a line under this scandal, and time limit cut-offs already exist for PPI claims. Before even thinking about a new time bar, the banks should be proactively contacting their customers and making it as easy as possible for people entitled to a legitimate refund to claim back their money, without any hassle."

He also called for a crackdown on claims management companies, which have been bombarding people with unwanted calls and texts. "Many people don't realise there are simple easy-to-follow steps to reclaim their money for free. The Government must now act to clamp down on unscrupulous CMCs and concentrate on reforming the banks."

Jon Slater, spokesperson for the Robin Hood Tax Campaign, which wants a tax on banks' financial transactions, said: "Rather than trying to wriggle off the hook they have got themselves on, banks should face up to their responsibilities and pay to repair the damage they have caused. If the banks aren't willing, the regulators should make them."

Such a furious response from banks' critics could make it tough for regulators to impose any new time limit, which could only come after a three-month consultation, making a date of May 2014 highly unlikely.

The FSA, which is changing to the new Financial Conduct Authority, could find itself engulfed in a huge controversy if it took such a step. It could also be subject to a legal challenge.

Bodies such as the CBI and even the Bank of England have become increasingly alarmed at the cost of the PPI scandal, fearing it could be preventing banks from lending to business. The Bank's Financial Policy Committee has voiced worries that compensation payouts are eating into banks' capital resources at a time when regulators want them to strengthen their balance sheets to protect them from economic shocks.

A spokesman for the BBA said: "The BBA and its members are committed to improving trust and confidence in banking, and we want to ensure that where customers have been mis-sold that they should receive all the compensation that they are entitled to. We have been in discussions with the FSA about proposals to ensure that those customers who are entitled to compensation receive it as quickly and simply as possible."