John Jackson, chairman of the committee of independent directors of Pilot Investment Trust, said the actions of the Bank's pension fund smacked of "gross short-termism".
The Bank's pension fund, whose trustees include Frances Heaton, Bank director, and Dame Sheila Masters, head of KPMG's public sector practice, was the largest shareholder in Pilot with a 12 per cent stake.
But it sold that stake after the investment trust received an unsolicited bid of pounds 46m from Undervalued Assets Trust, a fund run by Colin McLean.
In a letter sent to shareholders at the start of the week Mr Jackson described that bid offer as a "low ball attempt by Undervalued Assets Trust to obtain control of your assets".
He told shareholders the assets were significantly undervalued relative to their potential and urged shareholders not to sell.
Pilot's net asset value at the end of February was pounds 54.24m. It was set up to invest in small quoted companies, some of which lent their support to Pilot in letters to the trustees of the Bank's pension fund.
Douglas Rogers, chairman of Barcom, a construction equipment company, wrote to Mrs Heaton, pointing out the important role Pilot played in financing small companies.
"Small companies, if they are to continue to grow and provide improving employment prospects, need the long-term capital and support that Pilot provides," Mr Rogers wrote.
"I find it extraordinary that the Bank... attempts to promote long-term banking attitudes but allows its pension fund, which ought to have a long- term perspective for the benefit of current members, to jeopardise the existence of a true provider of long-term capital."
A spokeswoman for the Bank declined to comment.Reuse content