Consumers are being promised a "hassle-free" account switching experience when the new pledge, which covers almost all of the current account market, takes effect from Monday.
When customers change accounts, their new bank will be held responsible for all existing payments being moved over with the account, and any new payments accidentally made to the old account will automatically be redirected for 13 months.
The length of time it takes to switch will be cut from up to 30 working days to seven, and interest and charges will be refunded if anything goes wrong under the initiative, which is being overseen by the Payments Council.
There have already been some signs of banks ramping up competition in preparation for people to make the jump, while comparison websites have reported a rise in activity from people searching for current accounts.
First Direct recently increased its cash incentive to switch to £125, while Halifax is offering £100 and M&S Bank is handing out £100 worth of gift cards to new customers. Halifax also reported last week that it is on track to see 300,000 customers switch to it in 2013.
He said: "It is going to take a long time to break the mould and it will take a lot of effort from the challengers."
Current levels of switching are generally low. This 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 recent report from the Office of Fair Trading (OFT) found that the country's biggest current account providers - RBS Group, Barclays, HSBC, Lloyds Banking Group (which owns Halifax), Santander and Nationwide, had more than a 90% market share in 2012.
It found the combined market share of smaller providers has dropped off in recent years, as the economic downturn took hold.
Mr Mountford said that in the coming months, banks will need to work to introduce new products and improve their customer service to encourage more people to switch.
The success of the new switching scheme will not be reviewed until 2015, to give it time to bed in. The Payments Council has not set a target for the number of people expected to switch and it has said it will judge its success on criteria such as consumer awareness and improved confidence in switching.
Existing current account providers will face new competition in the coming months from Tesco Bank and Virgin Money, both of which plan to enter the market soon. A spokesman for Virgin Money said it is still working on its proposition and no launch date has yet been set.
David McCreadie, managing director of banking at Tesco, said development of its current account is "well advanced" and it will launch in 2014.
Meanwhile, it is also understood that Lloyds, which recently shed more than 600 branches as it broke off from TSB, is preparing to unveil a new customer loyalty rewards scheme in the near future.
There have already been some signs that consumers' appetite for switching is increasing. Comparison website uSwitch has reported seeing a 25% month-on-month increase in current account page views in August.
There has also been a 49% increase in consumers clicking through to current account providers' websites over the same period.
Michael Ossei, personal finance expert at uSwitch, said: "From what we have seen so far, First Direct, Nationwide and Santander are the front-runners in the battle to win over customers."
Mr Mountford said that some accounts already stand out as offering particular value, depending on individual circumstances.
For people who tend to remain in credit, Mr Mountford highlighted Lloyds' Vantage account and Santander's 123 account, both of which offer in-credit interest of up to 3%. For those who are often overdrawn, the Post Office has a relatively low overdraft rate of 14.9%, while First Direct also offers an overdraft at 15.9%.
Rachel Springall, spokeswoman for website Moneyfacts, also predicts that consumers are likely to see banks improving their savings deals and offering more discounts in the coming months to try to retain existing customers and tempt new ones in.
She said: " The new switcher guarantee should encourage customers to revisit their existing current accounts and weigh up whether it's providing them with value for money or not."