Key figures from both Tory and Labour benches last night called on the Government to amend the Bank of England Bill, which deals with the key issues of the Monetary Policy Committee (MPC) and banking supervision.
Giles Radice, the Labour chairman of the Treasury Select Committee, said MPs should be allowed to assess the credentials of MPC candidates.
Mr Radice said: "I think it is essential that the Monetary Policy Committee be seen to be competent, effective and independent".
But the MP stressed he was not seeking the power to veto MPC appointments. Rather, Mr Radice wanted to be able to endorse suitable candidates and to ask the Chancellor to reconsider the appointment of candidates deemed unsuitable.
Quentin Davies, a Conservative MP and Select Committee member, argued for a stronger amendment which would give MPs a say in the appointment of the Governor and Deputy Governors of the Bank.
Mr Davies said the amendment would provide a "vital check and balance" and would help reassure those worried that the Chancellor would merely give jobs to his "cronies".
These worries were echoed by David Heathcoat-Amory, shadow Treasury Chief Secretary, who said Select Committee confirmation of appointments would ensure candidates "measure up to the full standards of expertise and impartiality which the House expects".
Michael Fallon, shadow trade and industry spokesman, also argued that "this Quango Bank" should be more accountable.
But Alistair Darling, Treasury Chief Secretary, argued there were serious practical problems in allowing MPs a say.
Although Mr Darling conceded the "calibre and quality of its members clearly matters" he said the Chancellor was "bound to appoint only those people who have sufficient expertise and knowledge".
Mr Darling added: "If Select Committees are to be given the power of confirmatory hearings and - almost by definition - the power to choose who might or might not be on the MPC, then one could imagine a situation where the MPC appointed might not be the appointees of the Chancellor but in fact the appointees of the select committee or perhaps the House itself. There is an issue of principle here."
The Bill, which followed Labour's surprise announcement in May, hands operational policy for the setting of interest rates to the MPC, which lies within the Bank of England.
According to the Bill, the MPC should consist of nine members - the Governor of the Bank of England, the two Deputy Governors and six others. Four of these other members are appointed by the Governor, after consultation with the Chancellor. The other two are appointed directly by the Chancellor, as are the Governor and the Deputy Governors.
Currently, the MPC consists of Eddie George, the Governor, David Clementi, a Deputy Governor, Sir Alan Budd, Willem Buiter, Charles Goodhart, DeAnne Julius, Mervyn King and Ian Plenderleith.
Mervyn King, the Bank's executive director, will become a Deputy Governor after the Bank of England Bill becomes law.
The MPC has been responsible for setting interest rates since June, and, since it was handed the reins, has increased rates four times.