Some 65% of the new Cabinet attended an independent school, including Mr Sunak, who went to Winchester College, along with his three most senior colleagues: Chancellor Jeremy Hunt (Charterhouse School in Surrey), Foreign Secretary James Cleverly (Colfe's School in Greenwich, south-east London), and Home Secretary Suella Braverman (Heathfield School in Pinner, north-west London).
The proportion is broadly similar to Ms Truss's cabinet (68%) and Mr Johnson's first cabinet (64%), but much higher than the level in Theresa May's 2016 cabinet (30%).
It is also up on the figure for David Cameron's 2015 cabinet (50%) and well above the 32% in Tony Blair and Gordon Brown's cabinets, though close to the 62% in the Conservative-Liberal Democrat coalition in 2010.
The analysis has been published by social mobility charity The Sutton Trust, and it also shows nearly a quarter (23%) of Mr Sunak's Cabinet went to a comprehensive school while one in 10 attended a grammar school.
Among those who went to a comprehensive are leader of the Commons Penny Mordaunt, Transport Secretary Mark Harper and - perhaps symbolically - Education Secretary Gillian Keegan.
Sir Peter Lampl, founder and chairman of the Sutton Trust, said: "Rishi Sunak faces unprecedented challenges as he enters Number 10.
"In his new Cabinet, 65% went to private schools - over nine times the number in the general population - and 45% went to Oxbridge, more than double the average for all MPs.
"While his Cabinet is marginally more representative than Truss's, Tuesday's appointments highlight how unevenly spread opportunities to enter the most prestigious positions continue to be.
"Making the most of Britain's talent regardless of background must be a priority."
Mr Sunak continues the tradition of nearly every UK prime minister since the Second World War having studied at Oxford University.
The one exception is Gordon Brown, who went to Edinburgh University.