The new voluntary code, which is being incorporated by Lloyds Banking Group, HSBC, Nationwide Building Society, Barclays, Santander, the Co-operative Bank and NatWest among others, will mean that as soon as someone tells their bank they have made a mistake with a payment, they will act within two working days.
If the bank cannot reclaim the funds immediately, for example if the payment recipient disputes the return, it will investigate further and the customer will be told within a maximum of 20 working days what the outcome is.
Someone who raises a claim for a wrong payment is not guaranteed that they will get their money back under the new rules and people are still being warned to "check before you click" when transferring cash.
But the Payments Council, which is overseeing the code, said it would put that person in a better position as they would find out where they stood more quickly and they could then take their complaint further.
The other banks and building societies who are signing up to the code are Clydesdale Bank, Coventry Building Society, Coutts, Tesco Bank, the Royal Bank of Scotland, Yorkshire Bank and Adam & Company.