The move follows a similar decision taken last year by HSBC and means two of the largest credit card provider are restricting access to loans – the latest example of British banks refusing to lend money to anyone but the safest customers, despite being implored to lend money to consumers by the Treasury.

Those who want to apply for a NatWest/RBS credit card must have a current account with one of the banks. Having a mortgage or savings account from the group will not be enough. The change took effect on October 1.

Louise Bond of uSwitch.com, the price comparison service, said others could follow suit, leaving consumers with less choice.

“This isn’t the first time we’ve seen a credit card provider do this and I certainly don’t think it will be the last. This move minimises the risk for banks but at the same time it also limits consumer choice,” she said.

“With a market-leading 15-month 0 per cent balance transfer credit card, it’s quite disappointing that the deal is open only to customers who have an RBS current account,” she said. “Given that the RBS fee-free current accounts pays just 0.1pc interest on credit balances and charges 19.24 per cent on overdrafts, this is uncompetitive to say the least.”

Both HSBC and NatWest/RBS are in the top five of the biggest cred card lenders, with a signifcant share of the 66.1 million cards outstanding in Britain.

Many people rely on credit cards as their main source of borrowing, with £139 billion spent on credit cards last year – the equivalent of £3,088 for every adult in the country.

According to the Bank of England the average interest rate on a credit card is now 18.13 per cent — the highest rate since records began a decade ago, despite the Bank rate being at an all-time low of 0.5 per cent. Experts say this is further proof that lenders are tightening terms, even though the economy is showing signs of improvement.

The trend towards offering the best deals only to existing customers was also appearing in the personal loans market, Ms Bond said.

A spokesman for RBS, which is majority-owned by the taxpayer, said: “We are focusing where we can on helping our current account customers, savers and mortgage borrowers and this move helps us improve the service we can provide to them.

“We are very much open for business and welcome new customers who want a current account and a market leading credit card from us”.

HSBC confirmed it is only offering cards to existing customers. It said this had been the policy since the worst of the recession hit last year.

A spokesman for the UK Payments Association, which represents the card card lenders, said that competition would remain, but admitted tighter terms were “a reflection of where the market is at the moment.”