Credit card companies are facing an investigation by competition watchdogs after defying government warnings to improve their lending practices.

An analysis by The Independent has found that the cost of card borrowing has risen over the past three months despite three cuts to the Bank of England base rate. Cardholders are now facing average interest rates of 17.7 per cent on credit cards, up from 16.6 per cent 12 months ago.

The Business Secretary, Lord Mandelson, had given providers two weeks to come up with fair principles to help cardholders manage their debts following a summit with card providers in November. By Thursday, the Government is expecting proposals from the industry on how it will implement fair principles on existing debt, responsibly provide credit and support households in difficulty.

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Failing to do so could see the card companies facing investigation by the Office of Fair Trading (OFT), but so far card providers have made no move to reduce the expensive lending rates which so often plunge debtors into further financial hardship.

One government source said last night: "We are not backing off. If the companies don't move, if necessary, we will go down the OFT route."

Only two cards, those designed to track the base rate, have reduced rates since Lord Mandelson's ultimatum and Yorkshire Bank and Clydesdale Bank have gone ahead with increases to the rates and fees they charge their Gold Mastercard customers. Halifax and the Bank of Scotland have also increased balance transfer fees.

A spokesman for Clydesdale Bank said: "The changes in our rates were announced in October and our rates remain very competitive. We fully support the Government's initiatives for helping people in difficulties."

Store card debtors are facing even higher rates despite cheaper borrowing for lenders. The average cost of borrowing is now 25 per cent a year, up from 23.9 per cent this time last year, with no sign of a cut in rates even though the base rate has dropped from 5.25 per cent to 2 per cent over the same period.

But based on the industry's response this week, Lord Mandelson and the Consumer Affairs minister Gareth Thomas are expecting to produce a plan to address the dramatic increases in some cardholders' bills.

A spokeswoman for the Department for Business, Enterprise and Regulatory Reform said: "We've asked lenders to report back by the end of this week and have been in continuing talks with industry following our summit [on 26 November]. We have every expectation that industry will come back with proposals to stop the pockets of bad behaviour that we have identified in risk-based repricing and will continue to work with them to ensure borrowers are treated fairly, responsibly and consistently."

Vince Cable, the Liberal Democrats' Treasury spokesman, said: "The Government has got to get tough with credit card companies determined to make a quick buck out the millions of people struggling to make ends meet. Tough words are worthless unless they are backed up with real action."

Alan Duncan, the Conservatives' business spokesman, accused ministers of pumping out "hot air". He said: "The Government's policy after the banks' bailout has clearly not reached the credit card sector. It has done nothing to clamp down on credit card ownership – particularly by the most vulnerable people."

Industry leaders have been summoned to another meeting with Mr Thomas on Thursday.

Apacs, the UK payments association, denied interest-rate rises were the problem. "Risk-based pricing is not about the base rate at all," said a spokeswoman. "This is about a customer with a card whose APR may go up as a consequence of changes to their circumstances. It is a feature of credit cards that the interest on this unsecured borrowing may be adjusted. If the customer can't pay, the provider has no security on getting the money back and may decide to re-price the cost of using the card. The agreements that were made [at the summit] were about breathing space for customers in difficulty."

Critics of the move believe a half-hearted approach will make little difference to consumers. Martin Lewis, of Moneysavingexpert.com, said: "This ultimatum is absolute nonsense, and shows that Lord Mandelson has never had any connection to credit cards in his life. Is he saying that credit card companies should drop their interest rates in line with the base rate drop, from an average of 18 per cent to one of 15 per cent? To make this work they would actually have to cut their interest rates by 60 per cent to mirror the real changes in the base rate, so if even if every credit card on the market took 3 per cent off their interest rates it would mean nothing."

Credit and store card companies have long been accused of employing dirty tricks to boost income. The order of payments is regularly skewed so that the most expensive debt, with the highest interest rate, is paid off last.