Link, the cash machine network, revealed three high street banks were in advanced talks on joining Link. The aim is create a unified network of machines for the whole country.
Barclays, Lloyds Bank and Midland Bank are planning to become members of Link by the end of May, giving customers access to around 25,000 machines. National Westminster Bank will also become a full member.
John Hardy, chief executive of Link, said: "This is a significant move in the expansion of Link and it will create a single national network of cash machines, providing access to virtually all banks and building societies in the UK."
The big four high street banks have historically avoided a unified network, choosing instead to use the size of their networks as a way of attracting new customers.
Customers with Midland and National Westminster Bank share access to 12,500 machines, while Lloyds and Barclays share a network of 7,600. Link, including building societies and mortgage banks, has 15,400 machines.
Bank customers have generally been blocked from using machines in a rival network. Where they can use them, the typical charge is pounds 1.50 per withdrawal.
A survey by Mori showed that 77 per cent of all age groups - and 92 per cent of those under 35 - wanted to be able to use any cash machine. Britain is one of the only countries in the world without a unified network.
The move came out of talks held to discuss the need to update systems to cope with the Millennium Bug, according to a Midland Bank spokesman. He said banks decided to discuss what other changes might be made to cash machines.
However, Mr Hardy said some banks were likely to continue charging customers for using Link machines. NatWest and Woolwich, for example, charge 60p for each transaction.