A majority of voters favour reform of the House of Lords, according to a poll that will boost the position of Nick Clegg who is fighting a growing Tory campaign to maintain the status quo at Westminster.

As a joint parliamentary committee unveils its plans for a mainly elected second chamber, a YouGov poll commissioned by Unlock Democracy found that 69% of voters support a reformed House of Lords. The poll found that just 5% of voters favour the status quo – a fully appointed second chamber.

The highest number of voters (33%) said they favoured a fully elected second chamber – the official position of the Liberal Democrats and Labour in their 2010 election manifestos.

A fifth of voters favour a chamber with equal numbers of appointed and elected members. A slightly smaller number of voters (16%) favour a mostly elected chamber with a small number of appointed members – the position adopted by the Tories in their 2010 general election manifesto.

A small number of voters (5%) favour a mostly appointed chamber with a small number of elected members. The same number of voters support the status quo – a fully appointed chamber.

Unlock Democracy said the poll showed a clear majority in favour of reform. Peter Facey, director of research, said: "The three major parties all committed themselves to democratic reform of the House of Lords at the last general election; they cannot spin or dissemble themselves out of this commitment. And while it may not be on top of everyone's agenda, polls have consistently shown that the public support Lords reform themselves."

Unlock Democracy is releasing its poll to coincide with the publication of a report by a joint parliamentary committee which is expected to call for a second chamber in which 80% of members would be elected. The final 20% would be appointed. The committee is also expected to call for any proposals on reform of the second chamber to be put to voters in a referendum. This is one of the main demands of backbench Tory opponents of reform who have won the support of five cabinet ministers, including the education secretary, Michael Gove, and the defence secretary, Philip Hammond.

Tory opponents of reform opened up a new flankon Sunday by saying that a referendum on Lords reform would have to be accompanied by a vote on Britain's relationship with the EU. Mark Pritchard, secretary of the backbench 1922 committee, told BBC1's Sunday Politics that it would be "very difficult" to hold a referendum on Lords reform and deny one on the EU.

The referendum may become a source of tension between Clegg and David Cameron. The deputy prime minister once again rejected a referendum, which is being supported by Ed Milband. But the prime minister is indicating to Tory MPs that he might be open to the idea.

Clegg told BBC1's Sunday Politics there was no reason to hold a referendum because the three main parties had each advocated Lords reform in their manifestos.

"Let's remember, all three parties, Labour, Liberal Democrats and Conservatives, had a manifesto commitment for Lords reform. To sort of subcontract to the British people an issue which the politicians at Westminster just can't deal with, I think is asking a lot of the British people when of course last year we did have a referendum. But that was an issue where there was very stark difference of opinion between the different political parties. That's not the case here."

The Unlock Democracy poll found strong support (62%) for giving the public the right to trigger referendums by collecting signatures on a petition. A smaller number (22%) thought this power should rest with parliament and the government.

The poll also found support for the reformers at Westminster. It found that 48% of voters believe that peers should not be allowed to block the reforms if they are passed by MPs. A fifth of those asked said that peers should have a veto.

Ministers have indicated they would be prepared to use the Parliament Act to force through the changes if they are blocked by peers. Opponents of reform are increasingly confident this will not be necessary because they believe the reforms will become bogged down in the Commons. The poll also found that 45% believe that experts should be invited to help shape laws on a case-by-case basis, in committees and debates rather than allowing them to become full members of the second chamber. A smaller number (32%) said experts should be invited to become full members.

YouGov interviewed 2,349 adults online between 18-20 April. The figures were weighted as representative of all British adults aged over 18.