A motion by the Local Authority Pension Fund Forum to appoint an independent chairman by next July received the support of only 37.7% of shareholders.
The motion would have had to receive the support of 75% of shareholders to be passed.
M&S says: “The board sees this as an endorsement of its succession process and we will proceed as planned”.
Sir Stuart has already said he will step down as chief executive in 2010, continuing as chairman before withdrawing from the retailer entirely by July 2011.
Criticism about his dual role has been mounting since last year’s AGM from shareholders who say it demonstrates poor corporate governance. He has also come under increased pressure following slowing sales and falling profits.
Last month, he and marketing director Steven Sharp said they were to forego a third of their long-term bonuses following criticism from the Association of British Insurers.