Royal Bank of Scotland (RBoS) yesterday announced it had signed a deal with Link, the building society cashpoint network, which gives the bank's 2.5 million customers access to all Link machines.
RBoS described the deal as the "final piece of the jigsaw", allowing its customers to use the UK's entire cashpoint network.
Harry Hay, the bank's head of cashline network development, said: "This underlines the bank's commitment in continuing to provide a first-class customer service and is very much a result of listening to all cash machine cardholders.
"Our research shows that people want to be able to access their cash as simply and conveniently as possible. However, it has shown that very few know where they can use their cash cards and often shy away from machines they are unsure of to avoid the embarrassment of the card being rejected."
RBoS, which has just 1,300 cashpoints of its own, already has arrangements with all the traditional banks offering cashpoint networks. The arrangement also applies in reverse - customers from any bank or building society can now use an RBoS machine.
A survey by Mori, commissioned by the bank, showed that 77 per cent of all age groups, and 92 per cent of those under 35, wanted to be able to use any cashpoint. Cashpoints were the most popular service a bank could offer, the survey said.
RBoS's move will exert pressure on other banks and building societies which have resisted customer pressure to bring their networks together.
The UK is the only place with a cash machine network where bank customers cannot use any cash machine, a facility known in the US as "universal reciprocity".
Most Lloyds Bank and Barclays Bank customers can use neither Midland nor NatWest cash machines because of a reluctance by the big banks to come to an agreement on how much they must charge each other to serve rivals' customers.
A Midland spokeswoman said the main obstruction to a combined network was the issue of charges. Unless customers could use another cash point free of charge, they did not want a larger network, she said.
A Lloyds Bank spokeswoman said: "There is no customer demand for access to more machines at the moment."
Some former building societies on the Link network, such as Halifax, charge their customers if they use a cashpoint machine at a smaller bank such as Woolwich.
Many new cashpoint cards at English high street banks are attached to the Cirrus network. This gives access to other networks, but for a fee.
Some observers believe that behind the reluctance of the two biggest networks, Midland/ NatWest and Lloyds TSB/Barclays, is a belief that they can gain more by promoting their cashpoint network as larger than their rivals' than by offering an integrated network.