They will receive a six digit pin number after making the request, which can be entered at a cash machine for the money to be released.
The scheme aims to help people who may have lost or forgotten their card or those who might want to leave their wallet at home.
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The service, named GetCash, works at NatWest and RBS ATMs, with a limit of £100 per use. The pin codes issued are valid for three hours and people can use the scheme as many times a day as they need to, as long as they do not go over their withdrawal limit.
It is available to around two and-a-half million customers who already have the banking app on their phone and those behind the initiative said it is a first for the UK.
Ben Green, head of mobile at NatWest and RBS, said: "We've heard countless stories from customers who've left their wallet behind, or parents who need a quick way to send money across to their children immediately."
Customers can access the banking app on iPhone, iPad, Android and Blackberry Smartphones.