The Bank of England faced questions over its handling of the rate-rigging scandal last night after it emerged it was warned the system was open to abuse four years ago.

American regulators urged the bank's governor, Sir Mervyn King, to ensure it could not be manipulated in 2008.

The lobbying emerged amid reports banks could face fines of up to $22 billion for their part in the affair.

Barclays has already lost its chairman and chief executive after it became the first institution found guilty over its involvement in fixing a key interest rate.

But there were increasing questions last night about the Bank of England's actions.

Emails show the then New York Federal Reserve president Timothy Geithner urged Sir Mervyn to prevent "accidental or deliberate misreporting" of the rate.

Mr Geithner even set out a raft of proposals in June 2008 to reform the interbank lending rate, also known as Libor.

The rate is crucial because of the knock-on effect it can have on the rates at which banks then lend to their customers.

The emails show that Sir Mervyn supported the suggestions, writing to Mr Geithner that they "seem sensible to us".

And he said that they would be put to the British Bankers' Association (BBA) – which runs Libor.

Stewart Hosie, the SNP's Treasury spokesman, said: "Reports that Timothy Geithner pressed the Bank of England to make changes in the way Libor was set in 2008 escalate the questions over who knew what and why action was not taken earlier on the rate-rigging scandal.

"We need to know how detailed the discussions were between central banks, between the regulators at the Financial Services Authority and their US counterparts, as well as between Ministers and Officials at the Treasury."

Sir Mervyn is expected to be quizzed about the emails when he appears in front of MPs next week.

Meanwhile the Tory-Lib Dem Coalition announced the make-up of its newly created parliamentary inquiry into the scandal, but immediately ran into controversy after one MP denounced it as a joke.

John Mann, the Labour MP who sits on the Commons Treasury Committee, also announced plans to set up a rival probe.

Those who were named as members, LibDem John Thurso, Tory Mark Garnier and two Labour MPs, Andy Love and Pat McFadden, are all also members of the Treasury committee.

It will be headed by that committee's chairman, the respected Tory MP Andrew Tyrie.

But it almost immediately faced criticism for including no women and for taking all of its MPs from the Treasury committee – but ignoring two of its most prominent members. Yesterday Downing Street denied that Andrea Leadsom, the Tory MP, had been blackballed for comments she made at the weekend suggesting that the Chancellor should apologise for saying Labour's Ed Balls had questions to answer over the scandal.

A Number 10 spokesman insisted that the membership had been agreed between the parties.

But Mr Mann, who embarrassed Mr Osborne earlier this year by asking him when he had last had a pasty, condemned the membership as a total joke, and pledged he would create his own inquiry.

"Both Andrea and I were available for the Inquiry, and because we are too outspoken we have been blocked," he added.