The Financial Ombudsman Service (FOS) was deluged last year by new complaints about banks and other financial companies.
It received 576,000 complaints, which was a 38% increase on 2012, though the number eased off in the second half of the year.
In the last six months of the year, 76% of complaints were about payment protection insurance (PPI).
The chief ombudsman Tony Boorman said 56% of those were upheld.
"The extraordinary volumes of financial complaints we saw in 2013 now looks as if they're starting to level off at last - and that has to be welcome news for everyone," he said.
"But we're still a long way from being able to say that PPI is sorted once and for all.
"Over 1,000 people every day are still asking us to sort out PPI problems that they've not been able to resolve directly with their bank," Mr Boorman added.
The FOS is not the first port of call for complaints. It deals with people who are dissatisfied with the response their bank, insurer, credit card company, mortgage lender or investment company has made to their initial complaint.
The ombudsman pointed out that non-PPI complaints fell in the second half of the year by 8% from the first half, down from 60,807 to 55,747.
But the FOS said that its overall "uphold" rate for all complaints, of 51%, was still "stubbornly high", showing that financial services companies were still not dealing with their customers' complaints adequately.
Most complaints continue to be against the big banks, who mis-sold PPI polices to their customers on a massive scale.
In the last six months of 2013 the most complained-about firms were Lloyds Banking Group, Barclays, RBS, HSBC and the credit card firm MBNA.
The PPI scandal has now cost the industry so much money that more than £20bn has been put aside to cover repayments to customers, a sum that is likely to increase further.
Lloyds Banking Group alone has set aside £10bn to cover the cost of repayments.