He will be replaced by Philip Cushing, who was promoted to managing director last year, a shift that marginalised Mr Mackay's position.
Mr Mackay, 56, has been chief executive since 1991 and will be in line for compensation of around pounds 750,000. He also owns shares worth pounds 147,000 and options worth pounds 150,000.
Sir Colin will make the announcement alongside a slump in the company's full-year profits from pounds 228m to pounds 140m and a possible cut in the dividend. He is also expected to announce a timetable for the flotation of Bain Hogg, Inchcape's insurance subisidary. The company yesterday declined to comment on any of the changes.
Mr Mackay's departure has been seen as inevitable given the company's woeful performance. As the world's largest distributor of Japanese cars, including Toyota and Mazda, the company has been hit by the recession and the rise of the yen. It has issued a string of profits warnings in the last three years during which the shares have plunged from more than 600p in 1993 to 262p. In December the company was demoted from the FT- SE 100 index of leading shares.
This followed surveys which showed that fund managers were beginning to voice discontent about the way the company was being run. It was criticised for an unclear strategy and poor communication with the City.
The decision to remove Mr Mackay will have been made more difficult for Sir Colin, the former British Airways chief executive, as the two are good friends. Sir Colin invited Mr Mackay on to the BA board in 1993. Both are non-executives of HSBC, the banking group.
Mr Mackay is the third director to leave the board in the last seven months. Last July, David John, the head of Inchcape's world-wide Toyota business, quit to join BOC, the gases group. A month later chairman Sir David Plaistow stepped down earlier than expected. It was thought that institutional shareholders were putting pressure on the company to shake up its management.
Mr Cushing, 45, joined Inchcape in 1990 after spells with Norcros, Lego and Norton Opax, where he was chief executive. He was initially responsible for Inchcape's Singapore operations and was promoted to the board in 1992.
His subsequent promotion to managing director a year ago made him responsible for the day-to-day running of the pounds 1.4bn company while Mr Mackay was put in charge of strategy.
Mr Cushing was educated at Highgate School in London and later at Cambridge where he gained a first in economics.
In September Inchcape reported that operating profits for the half-year were 42 per cent down.
It has since announced a series of cost-cutting measures. Around 2,000 jobs have gone and the company decided to move out of its swish central London head office to a cheaper West London location.
The company is also reducing its exposure to the Japanese economy by building up its distribution network of non-Japanese cars such as Volvo and Jaguar. The flotation of the Bain Hogg subsidiary is expected to raise around pounds 250m-pounds 260m. Earlier reports had suggested that Inchcape was keen to sell Bain Hogg but was unable to find a buyer willing to meet its pounds 400m valuation.
If the company does cut the dividend the City will be looking for details on how the board intends to use the additional funds. The full-year figures are expected to show lower margins in the all-important motors division, with Hong Kong and the UK well down on 1994.