The Financial Services Authority was today considering whether to launch a full-blown investigation into the way Royal Bank of Scotland was run before the taxpayer took control last October, amid allegations of boardroom bullying and a "culture of greed" at the bank.

The fresh controversy, raised by the Labour peer Lord Foulkes and Liberal Democrat treasury spokesman Vince Cable, prompted the loss-making bank's new management team to plea for a chance to start turning it around rather than focusing on the troubled past.

Both politicians wrote to Lord Turner, the chairman of the FSA, to raise their concerns, which are now being reviewed by the regulator.

Foulkes, whose concerns were first reported in the Observer, has been told that non-executive directors were intimidated to keep quiet about the way RBS was run by Sir Fred Goodwin, who left at the end of January with a £703,000-a-year pension. Cable published information from a whistleblower about "lifestyle rather than business issues", which he described as a "culture of greed". He called on the chancellor, Alistair Darling, to stop the pension payments to Goodwin.

Cable's unidentified whistleblower described how:

• The lobby outside Goodwin's office was decorated with wallpaper costing £1,000 a roll.

• £5.3m was spent refurbishing a grade I listed building for his hospitality use.

• £100,000 a month was spent on part-time chauffeurs.

• Fruit was flown in from Paris.

Turner made it clear that it was not his job to stop Goodwin's pension. He told the BBC: "A misjudgment – whether it be a business misjudgment or whether it be what I think most people think Sir Fred Goodwin has committed, which is a misjudgment in not being willing to give back some of his pension – is not something for the FSA."

He admitted the FSA would be concerned if non-executives had not been given enough information. There were suggestions this weekend that the bank was involved in sub-prime lending despite its denials.

Turner said: "There is a duty on the executives to ensure that there are flows of information to non-executives so they are being given the data to perform their function. If there are issues there, we will look into them."

Foulkes has written to the FSA to ask it to consider "whether there was any intimidation of non-executive directors who had been asking probing questions which led them to believe they would not be reappointed if they continued to pursue such searching questions".

RBS insisted it was not aware of any evidence to support Foulkes's claims: "It is not an issue that has been raised by any non-executive director past or present with the company or indeed with the FSA."

The bank added: "If Lord Foulkes has any evidence to support the assertion, it would be in the interests of all parties if he shared it. The first the company heard of this letter was not from Lord Foulkes but from the Observer newspaper.

"It is critical that the new management of the company is allowed to get on with the job of fixing its problems and returning it to standalone strength. Only then will we be in a position to repay the support of the taxpayer."