The National Association of Pension Funds said that as a non-executive director of Egg, the internet bank, Higgs breached his own criteria on independence, having been a director and employee of Egg's major shareholder Prudential until December 1, 2000.
It was the latest setback for the recommendations, which both Sainsbury and Tesco have recently defied.
Higgs opposes the appointment of former executive directors as non-executives in the same company.
Yet Sainsbury announced the promotion of group chief executive Sir Peter Davis to chairman, and Tesco announced it was appointing executive deputy chairman David Reid to chairman.
A spokeswoman for Sainsbury said: "We have shown that some parts don't apply to us but we gave good reasons for the appointment." A spokesman for Tesco added: "In the sense that there is a principle to comply or explain, we have explained."
In January, Higgs set out measures aimed at beefing up the role of non-executives in the boardrooms of publicly listed UK companies.