Farmer is stepping down along with two other directors, John Houston and Peter Holmes, in a move that has heightened speculation he is the leading contender to buy the firm.
Dominic DiMarco, a senior Ford executive and Kwik-Fit board member, has been appointed Kwik-Fit's group managing director, effective immediately.
Ford bought the fast-fit chain in 1999 for an estimated £1 billion as part of a drive by the manufacturer to offer a 'cradle to grave' service for motorists. But in a major policy rethink announced this year, the firm is now concentrating on its core business to reverse losses on car making that have run into billions of pounds.
Goldman Sachs is helping evaluate the sale of the firm, Europe's largest maintenance and light vehicle repair business, with 2,400 service centres and more than 11,500 employees.
Farmer said: 'There are too many rumours in the media regarding my intentions over the future ownership of Kwik-Fit. In order to avoid any perceived conflict of interest that may arise, it has been agreed that I and my colleagues will not participate in the management of Kwik-Fit while the sale process is taking place.'
Malcolm Macdonald, a Ford vice president responsible for the sale, said: 'This action is consistent with the high standards of integrity shown by the three.'