Financial services firms received 2.11 million new complaints between July and December 2015, marking a 1.4% fall compared with the previous six months, according to figures from the Financial Conduct Authority (FCA).
The overall fall in complaints was mainly driven by a 10% decrease in complaints about current accounts and a 15% fall in complaints about savings accounts, the FCA said.
But complaints about payment protection insurance (PPI) increased by 6% during the period compared with the previous six months, with 932,298 new complaints recorded.
PPI remains the most complained-about product, followed by current accounts, other general insurance, credit cards and savings including cash Isas.
The figures also show that Barclays was the most complained-about financial services firm in the second half of 2015, followed by Lloyds Bank, Bank of Scotland, NatWest and HSBC. All five firms saw complaints reduce compared with the previous six months.
Matt Hammerstein, head of client and customer experience at Barclays, said: "Complaints are an important way for us to hear from our customers how we can improve our service and to learn where things are not working so that we can take action to put this right. But it is equally important that we focus on improving the service for the 99% of our customers who do not complain, delivering products and services that answer what they want and need from their bank in order to improve overall customer satisfaction.
"New customer benefits such as video banking, increased value through our Blue Rewards programme, and instant lending decisions are being delivered all the time, which offer the more personal and convenient service our customers have told us they are looking for. We know we have much more to do and we will keep working hard to address our customers' evolving needs."
The FCA said the total redress paid to consumers fell to £1.97 billion between July and December 2015 which is slightly lower than the £1.98 billion paid between January and June 2015.
Christopher Woolard, director of strategy and competition at the FCA, said: "Firms seem to have taken on board our previous feedback on levels of complaints and we are slowly seeing firms address these issues.
"However, firms still need to do all they can to reduce complaints and ensure that they are working in the best interests of consumers."
Here are the top five most complained-about products and services between July and December 2015, according to the FCA, with the number of complaints and the percentage increase or decrease compared with the previous six months:
1. PPI, 932,298, up 6%
2. Current accounts, 454,276 complaints, down 10%
3. Other general insurance, 296,505, down 3%
4. Credit cards, 132,988, up 9%
5. Savings, including cash Isas, and other banking, 67,546, down 15%
And here are the top five most complained-about firms, with the number of new complaints they received between July and December 2015 and the percentage reduction in these complaints compared with the first half of 2015:
1. Barclays Bank, 279,561, down 1%
2. Lloyds Bank, 230,041, down 1%
3. Bank of Scotland, 182,702, down 4%
4. National Westminster Bank, 135,262, down 7%
5. HSBC, 120,986, down 14%