Nick Clegg has endured his most hostile reception in parliament after Tory rebels joined forces with Labour MPs to try to drown out his speech arguing in favour of House of Lords reform.

In a highly organised operation, the rebels repeatedly interrupted the deputy prime minister after he described the current upper chamber as a "flawed institution".

The rebels are confident of defeating the coalition on Tuesday night after Sadiq Khan, the shadow justice secretary, confirmed that Labour will join them in voting against a "programme motion" for the bill. This would plunge Clegg's reform plans into turmoil because there would then be no parliamentary timetable for the bill, and the government's entire legislative programme would risk being disrupted.

In a sign of their confidence, the Tory rebels published a letter signed by 74 Tory MPs expressing "serious concern" about reforms. With Labour's support, only 50 rebels are needed to undermine the government's majority.

The deputy prime minister is proposing to replace the current house with a mainly elected second chamber, 80% of whose members would be elected on a regional list by 2025.

One ministerial aide has laid the ground for his departure by handing a letter to Patrick McLoughlin, the chief whip, confirming that he will rebel in the two votes on Tuesday night – on the "programme motion" and on the second reading of the bill. Conor Burns, the parliamentary private secretary to the Northern Ireland secretary, who is a close friend of Margaret Thatcher, later challenged Clegg in the Commons. He said: "Many of us fear that by electing the second chamber, by giving it the greater legitimacy he is talking about, we will end up creating a rival to this chamber rather than a revising chamber that we all want to see."

Burns intervened as Clegg said it was time to reform the upper house, 100 years after his Liberal predecessors started the process. Herbert Asquith, the Liberal prime minister, limited the powers of the Lords in the 1911 Parliament Act after peers blocked David Lloyd George's 1909 "people's budget".

Clegg told MPs: "No one doubts the commitment and public service of many members of the House of Lords. But dedicated individuals cannot compensate for flawed institutions, and this bill is about fixing a flawed institution."

The deputy prime minister said Labour and the Tories should support his bill because two of their heroes supported Lords reform. "The Labour party has long campaigned against privilege and patronage in the other place going back all the way to Keir Hardie's 1911 manifesto," he said.

Clegg also invoked Winston Churchill, who declared at the time of the Liberal reform attempts, while he was a member of the party, that he supported a democratic element in the upper house. "Churchill said: 'I would like to see a second chamber which would be fair to all parties. And which would be properly subordinated to the House of Commons. And harmoniously connected with the people.' He ended by saying: 'The time for words is past, the time for action has arrived'. I couldn't agree more, more than 100 years later."

Clegg's remarks prompted a rebuke from Nicholas Soames, Churchill's grandson and one of the leading Tory rebels. "Will he cease to quote Churchill on these matters since they relate to Churchill's views on the House of Lords at a time of great conflict between the House of Commons and the House of Lords? And as he grew up through his political life he dropped those views and had great reverence and respect for the institution of the House of Lords, something I suggest [Clegg] should have as well."

Margaret Beckett, the former deputy leader of the Labour party, challenged Clegg for arguing that Labour has supported reform for 100 years. "Will he also cease to say that the Labour party has supported reform of the House of Lords since 1910? What we supported in 1910 was abolition."

The deputy prime minister used Beckett's intervention to challenge Labour to abide by its manifesto commitment to support reform. "If the Labour party's views have evolved over the last 100 years, I hope she will confirm that it is a clear manifesto commitment from the Labour party not only to support the principle of House of Lords reform, but also to deliver it in practice."

Alistair Carmichael, the Lib Dem government deputy chief whip, was criticised in private on Monday night for failing to organise support for Clegg in the chamber. It took around 30 minutes for the first Lib Dem to support Clegg.

Stephen Gilbert, the MP for St Austell and Newquay, asked: "Does Mr Clegg not think that people watching this debate will be bemused? Back in 2010, they voted for three parties that had House of Lords reform in their manifesto, yet backbenchers in some of those parties are now trying to block it. It has been 101 years, and the people voted for it in 2010; let us get on with it."