ShareSoc, which campaigns on behalf of the interests of small investors, warned that large institutions could become privy to information not available to others.
Mr Anderson, manager of the £2.5 billion Scottish Mortgage investment trust, chaired the funds industry's Collective Engagement Working Group which is establishing the forum.
Backers include heavyweight UK investors such as Legal & General Investment Management and Strathclyde Pension Fund.
The aim of the forum is to allow investors to collectively engage with company management and directors with the aim of persuading them to develop long strategies.
ShareSoc chairman Roger Lawson has said: "This just looks like a new City club for a few major City institutions rather than a forum for collective and open engagement."
ShareSoc complained of opacity in the way that forum members would be selected.
It protested that there would be no representation on the forum from private shareholders even though their numbers often outweigh the top institutional investors on company share registers.
ShareSoc would instead like to see companies establish Swedish-style shareholder committees, independent of the board of directors and management committee, to engage with investors.
The aim of the Investor Forum, which has the backing of the likes of the Investment Management Association trade body, is to encourage companies to adopt long-term strategies.
There have been concerns in some parts of the investment sector, particularly in the wake of the financial crisis, that too many companies operate according to short term targets which are often linked to bonuses.