A so-called "Duke of Westminster tax" is being considered by the Liberal Democrats to target "unearned income" being passed down through generations by wealthy families.
The party has proposed a new "general anti-avoidance rule" which would outlaw the use of "contrived structures designed purely or largely to avoid tax".
The move follows the death earlier this month of the billionaire landowner the Duke of Westminster whose fortune, estimated by Forbes at £8.3 billion, will be inherited by his eldest son Hugh Grosvenor who is 25.
Lib Dem leader Tim Farron said: "Hospitals are having to cancel important operations while not enough money is being pumped into schools to help kids from poorer backgrounds get on in life.
"At a time when our public finances are being starved of funds by an increasingly right-wing Conservative government, it cannot be right that one individual receives £9 billion through complicated yet entirely legal trust funds.
"What a legacy the Duke would leave if his fortune was ploughed into an accelerated schools programme to improve the buildings where our children are educated.
"It is understandable that parents who have worked hard all their life want to leave something to their children.
"It is very different when big estates pass billions of unearned income down the generations."
The Duke of Westminster owned 190 acres in Belgravia, adjacent to Buckingham Palace and one of London's most expensive areas, as well as thousands of acres in Scotland and Spain.