Instead he joined the family firm and was sent to do a master's degree in business administration in New York. He was forced to take remedial maths to cope with the course and the disgrace ultimately gave rise to the belief that basic numeracy needs more emphasis in the British education system.
Education has always been a passion for David Sainsbury. He is chairman of the governing body of the London Business School, and in the past 30 years education and training have benefited from a number of his company's schemes.
The most recent project, whereby schools can "buy" equipment with vouchers given for reusing shopping bags, was born out of another area of weakness.
"Through my contact with schools I realised they had a real shortage of equipment and this scheme is a way of helping them," David Sainsbury says.
"The basic skills are fundamental to the economic performance of any country, " he says. "There is plenty of evidence now to show how British industry has suffered because of a lack of skilled workers on the shop floor."
His own shop-floor staff are given the chance to extend their education, at the company's expense. "Mr David", as he is known, is said to be a man of ideas, but admits that this wasn't one of his.
"The staff started educating themselves," he said. Watching the difficulties experienced by disabled customers, a number of Sainsbury employees started taking lessons in sign language. "Now we actively encourage staff to take courses relevant to their jobs, and offer time off to complete them. It has been very successful," he says.
He considers it ludicrous that decisions that will affect a person's career have to be taken at 16, when the majority have no idea how they want to make a living. "It does not make economic sense and lessens a person's enjoyment of life," he says. "The A-level syllabus needs to be broadened."
Giving everyone the opportunity to do well is important to David Sainsbury. His charitable trust, the Gatsby Foundation, funds many projects, including a number of technology training courses.
"The top 10 per cent, the academics in this country, can do very well, " he says. "But those with skills in other areas, have been neglected." General national vocational qualifications are "a step in the right direction" but there is plenty of scope for improvement.
During the 1980s David Sainsbury gave about Pounds 1 million to the Social Democratic Party but today the main beneficiary of his continuing flirtation with left-of-centre politics is Tony Blair's new Labour.