The commission, chaired by the Conservative peer Lord Wakeham, has decided the upper house should be given an "enhanced" role in scrutinising and criticising ministers.
Its conclusions, reported in the Sunday Telegraph, said the chamber should have a limited number of elected members - maybe around 100 out of 500 peers in all.
However, Conservatives claimed that the Prime Minister would be happy to see a House of Lords in which all the members were appointed.
All but 90 of the hereditary peers will lose their rights to vote this month when the first stage of reform is completed. The draft report said its final reform should give it extra powers to summon ministers, particularly in relation to decisions made in Europe.
"Parliament should have more of a role in holding EU institutions to account. In practice, this can best be achieved through enhancing its influence on ministers before decisions are taken in the council," the report said.
"The Second Chamber must have a high degree of political authority and independent judgement without threatening the pre-eminence of the Commons, significant independence from parties, adequate powers, continuity of membership to moderate swings in popular opinion and procedures that promote open and reasoned debate," it added.
Life peers would still remain for life but could be retired, keeping the right to speak but not to vote. They would be chosen by an independent appointments commission and would represent all sections of society.
The Church of England would keep its representation in the Lords, but the number of bishops would be cut from 26 to 16. There would be no similar quotas for other religions.
The Lords would retain the power to delay government bills for a year, but there would be new machinery for dealing with disputes between the Commons and the Lords.
Lord Strathclyde, the Conservative leader in the House of Lords, said the leaked proposals would "terrify" Downing Street and would probably not be adopted.
"It would give the second chamber more authority, more independence and more power and they will do everything they can to get rid of it," he said.
Lord Strathclyde said the Government should have reformed the House of Lords in one go rather than removing the hereditaries' voting rights as a first stage.
Lord Hoyle, a government whip, said the Conservatives could have reformed the House of Lords themselves if they had wanted to.
"Tony Blair is the first prime minister this century that has gone about the reform of the House of Lords. We could only do it in two stages, or else there would be no reform at all," he said.Reuse content