More than two-and-a-half million complaints about payment protection insurance (PPI) are to be re-opened amid concerns that firms may have unfairly brushed them aside, the City regulator has announced.

Banks, credit card providers and personal loan companies have agreed to look again at the old complaints from 2012 and 2013, which could have involved consumers being paid too little compensation or having their complaint unfairly rejected altogether, the Financial Conduct Authority (FCA) said.

It came just as some of the major banks announced large falls in customer complaints in the first half of the year, with a major driver in the reduction thought to be down to fewer PPI cases being brought.

Royal Bank of Scotland (RBS) and NatWest reported a 25 per cent decrease in complaints when comparing the first half of this year with the same period a year earlier.

RBS/NatWest recorded 215,993 complaints in the first half of this year, of which 123,086 were about PPI.

Barclays Group said that at 284,342 overall, its complaints for the first half of 2014 are down by more than one quarter (26 per cent) compared with the first six months of 2013.

Giving its progress update, the FCA said that firms have handled more than 13 million PPI complaints and an "unprecedented" £16 billion has been paid back to consumers since the start of 2011, making PPI the largest financial services redress exercise ever undertaken in the UK.

While the scandal has "significantly damaged public trust in financial institutions", in general, firms have made improvements to the way they handle complaints and their processes are more robust, the regulator said.

However, the FCA said that in 2012 and 2013 the proportion of complaints being upheld by firms in consumers' favour fell.

When the regulator carried out further investigations into why so many complaints were being rejected, it was not satisfied that that all consumers had necessarily been treated fairly.

Firms have been upholding around 70 per cent of PPI complaints, but by late 2012, the uphold rate dipped to around 60 per cent.

The FCA said the uphold rate has started to pick up again since it stepped in.

The two-and-a-half million complaints that are being looked at again were made to firms of varying sizes across the industry. Businesses supplied samples of the way they had handled complaints to the FCA, which has asked them to look at some cases again.

Martin Wheatley, chief executive officer, at the FCA, said: "Making sure anybody previously mis-sold PPI is treated fairly now, and paid redress where it's due, is an important step in rebuilding trust in financial institutions.

"In around two-and-a-half million complaints this was not necessarily the case so, at our request, firms will be looking at these complaints again."

The regulator hopes to scale back its intensive PPI work next year if complaint volumes continue to fall and firms continue to improve handling processes.

RBS/NatWest confirmed that a "main driver" of the reduction in overall complaints made to them is due to a reduction in PPI complaints being brought by claims management companies.

TRBS/NatWest said: "PPI continues to be a dominant factor in complaint volumes, but volumes are reducing."