Some 89,000 current accounts have been moved to new providers in the four weeks since the launch of a "hassle-free" switching service.
The Payments Council said the figure was 11% higher than the same period a year earlier and represented an "encouraging start". It added that the IT system on which the service was built was operating smoothly.
Under the new scheme, the length of time it takes to switch bank accounts has been cut from up to 30 working days to seven and all outgoing and incoming payments should automatically move to the new provider.
Since launch, the Council said feedback has shown that customers can help prepare for their switch by being ready to give their new bank or building society an up-to-date bank statement that shows their current address.
Customers should also have their existing debit card with them as this will help their switch commence by enabling banks to run the security checks that they need to undertake to protect customers.
Adrian Kamellard, chief executive of the Payments Council said: "Since its launch 89,000 switches have been successfully made by customers using the new simple, reliable and hassle-free account switching service.
"We never expected that every customer who is tempted to switch would rush out to do so at launch, but this is an encouraging start.
"This service is all about customers and the focus continues to be on them.
"Across the entire industry huge amounts of work continues to be put in to ensure that customers get the commitments made in the guarantee. It is by getting this right that we can deliver on the objectives of increasing competition and providing greater choice for customers."