The Association of British Insurers and the National Association of Pension Funds have said the issue of Mr Brown's pay, although mishandled by the company, is not serious enough to warrant shareholders voting against the management at the company's annual meeting at the end of the month.
The shareholder proposing the resolution is Pensions Investment Research Consultants, a corporate governance monitoring group. The resolution demands that British Gas reconsider the £475,000 pay deal awarded to Mr Brown last November. He also gets a performance-related annual grant of shares worth up to 125 per cent of his salary.
The institutions are crucial to the vote, holding just over 75 per cent of the company's shares.
Although the ABI has not issued formal advice, it is telling any of its members who contact it to vote against the resolution.
Richard Regan, head of investment affairs at the ABI, said: "It's important to support the incumbent management wherever possible. It seems that an adequate case has not been made for opposing the board at the present time."
John Rogers, secretary to the NAPF's investment committee, said: "Shareholders have to get away from the emotive issues and ask themselves what they are in this game for. It is to act in the best interests of their members and not on what they themselves might think is right or wrong.
"What has happened at British Gas is a move towards what shareholders are looking for: full disclosure of pay details and performance-related pay. These are two positive points."
Richard Giordano, British Gas chairman, has been visiting City institutions to dissuade them from voting for the PIRC resolution.
However, PIRC remains confident that the resolution will be supported by pension funds and City institutions. Alan McDougall, joint managing director, said: "People could easily guess the ABI would come out against the resolution."