The controversial proposal is part of a radical package from the influential think-tank Demos on reforms to the monarchy.
The sovereign should also be stripped of all political power and the Church of England separated once and for all from the State, today's report concludes.
The Queen will be briefed on the main findings this week and the recommendations are likely to be the subject of discussion at future meetings of the Way Ahead group, the body of senior royals and advisers considering reforms to the monarchy.
The drive for change was supported by a MORI poll for the Independent on Sunday, which found that 60 per cent of people thought the monarchy should be modernised. In addition, 49 per cent believed the Queen should relinquish her political role, including the right to dissolve Parliament.
The long-awaited report from Demos, which is headed by Geoff Mulgan, a member of Tony Blair's policy unit, will reopen questions about the future of the monarchy.
It has been co-written by Mark Leonard, a member of the Foreign Office's advisory committee Panel 2000, and is far more extensive than had been expected. It will increase pressure on the Prime Minister from backbenchers to consider changes to role of the Royal Family when the Government reforms the House of Lords.
In a wide-ranging package, Demos recommends that, on the death of the sovereign, there should be a referendum on whether or not the heir should succeed to the throne. If the people voted against the first in line then a second referendum would gauge public opinion about the next in succession.
The report argues that the Queen should lose all political powers. These include the right in theory to veto Bills, dissolve Parliament, appoint the Prime Minister and award honours.
The think-tank calls for the Church of England to be separated from the State and for the sovereign to relinquish the position of Supreme Governor. The authors argue that Prince Charles has already indicated his willingness to embrace other religions by describing himself as the "defender of faith", rather than "defender of the faith", the title held by the monarch since Henry VIII.
The funding of the Royal Family should be cut, the report says, and money allocated to the monarchy in the same way as to other government departments, with the accounts subjected to full scrutiny by a Commons select committee.
Other proposals include replacing the Royal Household with an "Office of the monarchy", staffed by civil servants, and an advisory body made up of members of the public. The report also calls for the royal family to send their children to state schools and to use the NHS to prove their commitment to public institutions.
Mr Leonard said the polls showed the British people wanted reform, and not just "superficial tinkering but real change". "We must allow the monarchy to prove that its legitimacy is based on public support rather than divine right."
Buckingham Palace said the report would be "read with interest, but any issues of constitutional reform would be a matter for Parliament to decide".
However, Downing Street sought to distance itself from the report last night. "The Prime Minister is an ardent supporter of the monarchy," Mr Blair's official spokesman said.Reuse content