Lord Myners, the City Minister, was last night under renewed pressure over how much he knew about the £16.9 million pension awarded to Sir Fred Goodwin, the former Royal Bank of Scotland chief executive.

The Times has learnt that Sir Tom McKillop, the bank’s former chairman, has written to the chairman of the Commons Treasury Select Committee, offering to provide fresh evidence after hearing Lord Myners’s testimony last Tuesday.

Sir Tom is understood to dispute what Lord Myners told the committee when he said that he was not informed about the size of Sir Fred’s pension pot during negotiations last October over the Government’s rescue package for the bank.

In fact, according to Sir Tom, Lord Myners was told exactly how much the pension was worth.

John McFall, the committee’s chairman, is understood to have declined Sir Tom’s offer to appear again before it.

However, the conflict between the two versions may force Mr McFall to reconsider, raising the possibility that Lord Myners himself could also be invited to appear before the committee again.

Another member of the committee, the Conservative MP Andrew Tyrie said last night: “If it were to transpire that Lord Myners has misled the committee on such a crucial point, in my view his position would be untenable.”

In his evidence to the committee, Lord Myners admitted that Bob Scott, who headed the remuneration committee at RBS at the time, told him on October 11 last year: “The pension will be enormous, you know that.”

He went on to tell George Mudie, the Labour MP, that the amount of Sir Fred’s pension was not disclosed to him until February.

Later in the meeting, pressed by Mr Tyrie, Lord Myners said that, despite being told that Sir Fred’s pension was large, he did not ask how much it was.

He added: “I did not ask roughly how much, and Mr Scott offered no further information at that time.”

However, it emerged last night that Sir Tom disputes this version of events.It is believed that he is prepared to state that, on the evening of October 11, Lord Myners was told by Mr Scott that Sir Fred’s pension pot was worth £16 million. It is believed that he would also testify that Mr Scott — an insurance industry veteran with a good knowledge of pensions — spoke to Lord Myners at least three times that day about Sir Fred’s pension.

Mr Scott is one of several RBS directors known to have given statements to the law firm Linklaters that directly contradict Lord Myners’s evidence to the committee. These statements are believed to set out the events in which Sir Fred’s exit from RBS was negotiated with the Government — whose negotiating team was led by Lord Myners.

Sir Tom is also said to be unhappy at Lord Myners’s claim that RBS directors constructed an “elaborate ruse” to mislead him about the pension. He is believed to argue strongly that it would have been impossible to sack Sir Fred — something that Lord Myners has frequently argued should have happened — because, while RBS’s takeover of the Dutch bank ABN Amro in 2007 turned out to be catastrophic, it was not technically a sacking offence.

The Treasury Select Committee’s hearings in the banking crisis have already led to the resignation of the former HBOS chief executive, Sir James Crosby, as deputy chairman of the Financial Services Authority. Sir James, a former adviser to Gordon Brown, was disclosed in one committee hearing to have sacked a whistleblower who had raised concerns over a reckless sales culture that led to the bank’s collapse.

Sir Tom declined to comment. Mr McFall was not returning calls last night.

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