Comparison website MoneySupermarket has reported a 45% increase in the number of visitors to its site looking to snap up a new current account following the changes, which mean that people can now ditch their old provider and switch to a new one in just seven working days.
Nationwide also said it has seen a 79% week-on-week uplift in the number of people initiating a switch of their current account to the building society, while First Direct, which often comes out on top of consumer service surveys, said the number of calls from people looking to switch is running at double the levels it usually sees.
The new customer pledge, which was launched on September 16 and covers almost all of the current account market, aims to ramp up competition and should ultimately mean providers offering better products and customer service for the UK's 49 million current account holders .
Kevin Mountford, head of banking at MoneySupermarket, said: "Despite the current account switch service still being in its infancy, the signs are encouraging judging by the number of people who are looking to switch current accounts.
For people who often have money sitting in their current accounts, Nationwide's FlexDirect account pays annual interest of 5% on credit balances of up to £2,500 for customers paying in £1,000 a month for the first year, with the rate reverting to 1% after this period.
Meanwhile, Halifax's Reward account pays £5 a month to customers who put £750 a month into their account and remain in credit throughout the previous month and Santander's 123 account offers cashback on household bills paid through the account and up to 3% in-credit interest.
Nationwide Building Society said the recent jump it has seen in people looking to switch to it follows a strong period of growth in its market share of current accounts in recent years, which coincided with several major scandals involving big banks.
A spokeswoman for First Direct, which recently topped separate customer satisfaction surveys by MoneySavingExpert.com and Which? said it is "delighted" with the uplift in new customer inquiries seen in the last couple of weeks. The internet and telephone-based bank is owned by HSBC.
There have been signs of account providers ramping up competition to tempt in new customers in recent weeks. First Direct is currently offering people £125 to switch banks while Halifax is offering £100.
Yesterday, Lloyds Bank upped the interest rate on its monthly saver account from 2% to 3% for new customers. But people can only take out this deal if they also hold a current account with Lloyds. Experts predict that more banks are likely to follow suit by improving products which are tied to their current accounts to produce an overall "package" of deals which will encourage consumers to switch.
As well as cutting the length of time it takes to switch accounts from up to 30 working days previously, the pledge means all outgoing and incoming payments automatically move over into the new account and the new provider is held responsible if anything goes wrong. A ny new payments accidentally made to the old one will automatically be captured by a central service and redirected for 13 months.
Previous levels of switching have been low, which is seen as a barrier to competition between banks, which use the relationship they have with current account customers to sell them other products.
A MoneySupermarket survey conducted before the launch of the switch service suggested that two-fifths of people will change their current account as a result of the new service.
The Payments Council, which is overseeing the switching rules, has not put a target on the number of people expected to switch and the success of the scheme will be measured on how much it raises levels of consumer awareness.
A spokesman for Santander said that last week was on a par with the busiest ever week it has seen for people switching to its flagship 123 current account.
He said interest in the account has been "phenomenal", adding: "We hope that will continue."
Steve Pateman, head of UK banking for Santander, said: "Many thousands of new customers have chosen to switch to Santander since the current account switching service was launched."