High Street banks say they are back to opening accounts for small businesses as normal after pressures amid the pandemic caused problems.
In October, start-ups told BBC News how they were being "stifled" at birth owing to difficulties in opening a business bank account.
The Treasury Committee of MPs demanded answers from the banks, including why potential customers faced long delays.
The banks have now told the committee that the situation has improved.
The committee's chairman, Mel Stride, said it would "keep a close eye" on the issue.
Some banks were closed to new applications from small firms during the height of the Covid crisis as they concentrated their stretched resources on existing customers.
This coincided with an increase in demand for business current accounts, to allow entrepreneurs to take advantage of bounce back loans - one of the government support measures introduced for businesses during the pandemic.
Some start-ups said their applications had "disappeared down a black hole".
They included Sophia Murday, who had set up a greengrocer in a previously-empty shop in Glasgow just yards from her flat.
She had been a customer of one High Street bank for 20 years, but her application for a business current account was delayed, then rejected. She then realised nearly all of the biggest banks were closed to new business customers.
UK Finance, which represents the banks, admitted there were delays but encouraged people to shop around for a new account.
The saga prompted the Treasury Committee to seek reassurances from six major banks - NatWest, Lloyds, HSBC, Barclays, Metro Bank and Santander - that they were committed to serving small businesses as the country emerged from lockdowns.
In their replies, a number of banks said they had seen a rise in complaints, but against a background of rising demand and their own staffing pressures owing to Covid.
"It is clear that delivering on bounce back loans at short notice rapidly increased the demand for business bank accounts at the same time as banks faced considerable additional work in delivering this extra support," said Mr Stride.
"It is good to hear from these banks that the availability of business bank accounts is now returning to pre-pandemic levels."
He said the committee would "keep a close eye" on the issue and on the commitment from banks to support small businesses as the UK started to move out of the pandemic.