The move follows Barclays' announcement that it will charge customers of other banks pounds 1 every time they use its machines. On Friday, the Nationwide threatened to sue Barclays unless the plan is withdrawn by Thursday. Barclays has pledged to contest any action.
Barclays and other banks could also face an investigation by the Office of Fair Trading into charges for the use of cash machines. The issue is likely to feature in the Government's banking review being conducted by Don Cruickshank, the former head of the telecoms watchdog. This is expected to come out with a scathing attack on the industry when it reports next year.
RBS is hoping for a ruling from its lawyers by the end of the month, when Link members convene for their regular meeting. They have been instructed to study Link's contract to see whether there are grounds for expelling Barclays.
RBS's anger is shared by some of the other 33 members of Link, which was set up in 1986 to develop a national network of free cash machines. Several others are said to be taking legal advice to ascertain what can be done.
A spokeswoman for RBS said: "We are monitoring the situation very closely and we would hope that some resolution will come to fruition through Link rather than litigation."
The Co-operative Bank, which was a founder member of Link, is trying to persuade other members to ask Barclays to drop the charge. However, given Barclays' insistence that the fee will be implemented next month, Link members opposing the charge may be left with no choice but to call for the expulsion of Barclays, which only joined the organisation this year.
"It's taken 15 years to build the network up, and it may be dismantled in 15 weeks," said a spokesman for the Co-op.
Most observers believe that Link could break up altogether unless it takes a firm line with Barclays. Some members have expressed dissatisfaction with Link's board, which has so far failed to condemn Barclays' action.
The Nationwide said it had only resorted to the threat of legal action after failing to come to a solution through Link channels.
One banker said: "A lot of banks are keeping quiet because they are chargers themselves."
At present, only RBS, Nationwide and the Co-op - none of which charge customers for cash machine transactions - have come out in opposition to Barclays. Most other members charge a disloyalty fee, which is levied on their own customers when they use other banks' machines.
Barclays argues that, because of its extensive cash machine network, it is in effect subsidising withdrawals made by customers of other banks. It also says that since customers will be made aware of the charge before they complete a transaction - unlike disloyalty fees which customers do not see until afterwards - Barclays is encouraging greater transparency. Opponents argue that their customers who use Barclays will be charged twice - once with a disloyalty fee and again with the new charge.