Eligible customers can apply until February 28, instead of August 25, and will be able to complete the switch until the end of June 2021.
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A further 200,000 RBS and National Westminster Bank accounts with turnover of up to £1mln are now allowed to switch too.
The bank noted that the extensions do not change the total number of customers targeted under the scheme, so it does not expect a change to its current financial outlook.
If the target is not met, RBS will need to make penalty payments capped at £50mln.
The scheme provides funding of up to £275mln to encourage customers of its Williams & Glyn subsidiary to switch to other banks in an effort to promote competition. It was established by the financial regulators in 2017 after RBS failed to spin off the Williams & Glyn arm.
"This has been blamed in the statement on the on-going Covid-19 pandemic but, in reality, switching levels were running well below target even before its onset," broker Shore Capital commented.
"This, to us, suggests that the competition authorities are trying to solve a problem that simply does not exist and that customers, despite considerable incentivisation, do not want to switch to an alternative provider that may not have the same product range and capabilities as RBS."
Shares rose 2% to 122.82p on Tuesday morning.
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