The report published by Equal Approach, looked at the secondary school background of FTSE 100 CEOs and chairs educated in the UK, and the universities they attended.
It found 28% went to either Oxford or Cambridge and 52% went to one of the prestigious Russell Group universities.
Dawn Milman-Hurst, chief executive of Equal Approach, said the findings were "disappointing".
"A lot of attention has been paid to the 'glass ceiling' and lack of female representation at board level; but we should also consider the 'class ceiling' which state-schooled pupils can find hard to break," said Milman-Hurst.
"It's time we restated our commitment to fair access in UK plc so that anyone can make it to the top of business, whatever their background."
The study found 60% of senior executives in the oil and gas industry were privately educated, as well as 57% of CEOs and chairs in the media industry. However, none of the leaders of the UK's biggest banks were privately educated.
"Diversity brings numerous commercial benefits," said Milman-Hurst. "As the most visible figureheads of companies, and leaders of the board and management team, chairs and CEOs have a key role to play in this."
