More than 900,000 "no frills" basic bank accounts were opened in the year to June, bringing the total number of the fee-free accounts open to nearly five million, Government figures show.
Since September 2016, the UK's nine largest banks have been legally required to offer fee-free basic bank accounts.
These accounts give people somewhere to have their income paid in, such as wages and any benefits, as well as a place from which to pay their bills, but they tend not to come with added features such as an overdraft.
The accounts are designed to improve financial inclusion for those who do not have a current account or who might struggle to open a standard account, perhaps because they have a poor credit history.
The nine banking groups offering basic bank accounts are Barclays, Clydesdale and Yorkshire Bank, Co-operative Bank, HSBC, Lloyds Banking Group (including Halifax and Bank of Scotland brands), Nationwide Building Society, RBS (including NatWest and Ulster Bank brands), Santander and TSB.
The Treasury said that for the second year running, Nationwide and Lloyds Banking Group opened the most fee-free basic bank accounts between July 2016 and June 2017.
It said Lloyds Banking Group accounts for almost half of the basic bank account market.
In total, there were just under eight million basic bank accounts open in June, the Treasury's latest figures show, including nearly five million accounts consistent with the new fee-free standards as well as other basic bank accounts that were consistent with previous industry agreements.
Stephen Barclay, the Economic Secretary to the Treasury said: "Making sure that everyone has access to the financial services that they need is at the heart of our plan to build a fairer society and an economy that is fit for the future.
"The Government has legislated to make sure fee-free basic bank accounts are available to those who need them and I am pleased to see that so many people - who might have previously been at risk of running up debt through bank charges - have access to a completely free account.
"It is important for a fair economy that banks continue to help all their customers to manage their finances confidently and responsibly."