The PSR proposed that banks must reimburse payments over 100 pounds ($107.39) in "authorised push payment" (APP) scams.
The maximum claim would be a million pounds per payment, though many banks have lower limits. The time limit on claims would be no less than 13 months.
"Consumers still need to take caution when sending payments, but these proposed measures will have the added protection that most of their larger payments will be automatically protected," the PSR said in a statement.
The bank from which the money was sent and the bank of the fraudster would split the reimbursement bill, the PSR said. Processing costs and fees charged to customers cannot exceed 35 pounds.
Bank customers lost 583 million pounds in APP scams in 2021, up by 39% on 2020, the PSR said.
It plans to introduce the new rule after parliament expands the powers of the PSR, expected sometime in the first half of 2023.
Some of the banks that would be affected by the new rule include HSBC, Natwest Group, Lloyds, Barclays, Banco Santander and Virgin Money.
PSR also plans to publish data on how the top 25 banks are reimbursing customers and their levels of fraud.
Currently 46% of customers get reimbursed for APP scams, largely footed by the sending bank, and the PSR expects this to rise to over 95% under its new rule.
Several banks have already agreed to check names of the person being paid by a money transfer between banks, and the PSR wants to roll this out more widely.
($1 = 0.9312 pounds)
(Reporting by Huw Jones; Editing by Lisa Shumaker)
By Huw Jones