A parliamentary report on House of Lords reform has recommended an upper house of 450 members serving for 15-year non-renewable terms, with 80% of members elected and 20% nominated.
As expected a majority of the members on the joint committee on Lords reform also recommended that the change be put to the public in a referendum.
Lord Richards, the chair of the committee, said a public vote should be held as changing one of the two Houses of the legislature was "pretty fundamental constitutional issue", even more so than the "tinkering" with the electoral system which was put to a referendum.
The government has argued that there is no need for such a vote as all three main parties had a commitment to reform the second chamber in their election manifestos.
However speaking on Monday morning ahead of the report's publication, David Cameron refused to rule out a referendum.
"Personally I don't see it as a very compelling case - it would cost a lot of money," he said.
"But we live in a democracy. Parliament is going to debate and discuss this. The committee is about to come and and say that a referendum would be a good idea so we don't rule it out."
The Labour Party has also said it would like there to be a referendum on the plans.
Dr Meg Russell, from UCL's Constitution Unit said pressure for a referendum would now become "irresistible".
"The referendum already has support from the Labour leadership and many Conservative backbench MPs. If pressed to a vote on the issue in the Commons, the government would almost certainly lose," she said.
"Nor can defensible arguments against the referendum proposal necessarily be found."
A YouGov poll for Unlock Democracy published today found that 69% of voters support a reformed House of Lords, while only 5% of voters wanted to see it stay as it is.
The committee accepted the majority of the coalition's proposals in its draft bill, but it said the number of members of the reformed chamber should have 450 members rather than the 300 initially proposed.
The creation of an elected House of Lords is an issue close to the heart of the Liberal Democrats, and on Sunday Nick Clegg delivered a thinly-veiled warning to Cameron that he must face down a major Tory rebellion over the plans.
The deputy prime minister pointed out that he had asked Liberal Democrats to support coalition measures they did not like, and others should act in the same "spirit".
The comments, on the BBC's Sunday Politics show, came amid reports that at least six Cabinet ministers would prefer to see the changes delayed.
Philip Hammond, Iain Duncan Smith, Michael Gove, Eric Pickles, Owen Paterson and Lord Strathclyde are said to be among senior Conservatives who have voiced doubts.The party's backbenchers are also threatening a mass revolt on the issue, with the potential for resignations by several ministerial aides.