The voluntary agreement comes as fears grow that bank closures mean some areas are in danger of losing any way of depositing or withdrawing cash.
The Association of Convenience Stores (ACS) welcomed the latest development.
The ACS 2021 Local Shop Report showed that customers believe two of the most valuable services offered in convenience stores are cash machines and post offices.
ACS chief executive James Lowman said: “Convenience stores trade across the heart of communities across the UK and we know that cash is still very important for a large proportion of our customers.
“We are pleased that LINK has outlined plans to review cash provisions when a bank branch closes but it is vital to also ensure areas which already do not have trading bank branches are not forgotten or left behind.
“The Government needs to act urgently and decisively on its earlier commitment to legislate to promote access to cash.”