Sir Ed Davey has urged incoming prime minister Andy Burnham to introduce proportional representation (PR) before the next general election, without holding a referendum on the issue first.

The Lib Dem leader said his party was willing to work with Burnham on changing the voting system, and if he was “serious about changing the way we do politics” then “my door is open”.

If Labour waited until after the next election to change the voting system, it might be “too late,” he said in a speech.

Burnham, who is set to be confirmed as Labour leader on Friday and prime minister on Monday, said last year, external: “There is nothing more unstoppable than an idea whose time has come, and PR’s time has come.”

But during his by-election campaign last month, Burnham suggested he would not change the voting system immediately if he became prime minister.

Last week, in a Reddit forum, he said would “seek to persuade my own party” of the need to include a commitment to electoral reform in Labour’s next election manifesto.

He wrote: “I am a strong supporter of electoral reform, partly because I believe it will enable the change to a more collaborative politics, and one that is less about point-scoring and more about problem-solving.”

More than 80 Labour MPs have signed an amendment to the Representation of the People Bill, external calling for a commission on electoral reform to investigate ways to ensure the voting system is “fair, representative and sustains public confidence”.

The amendment, which is also backed by Lib Dem MPs and others, has been tabled by Labour’s Alex Sobel and is set to be debated in the autumn, in what could prove to be an early test for Burnham on the issue.

The UK has a patchwork of different voting systems, external, with only the Westminster Parliament and local authorities in England and Wales retaining first-past-the-post (FPTP).

In a speech to the Institute for Government (IfG) think tank, Sir Ed argued that electoral reform was not a “nerdy obsession of political anoraks” but was key to “solving the problems that ordinary people face every day”.

“Our broken political system is the reason why so much in our country isn’t working the way it should, and why it never seems to get fixed,” he told the audience in central London.

He said his message to the incoming Labour prime minister was: “be bold, be brave”.

“Fix the broken electoral system by introducing proportional representation.

“To give everyone an equal vote and an equal voice in our democracy, and make sure no politician or political party can afford to take them for granted.

“And do it now. Don’t wait until it is too late. Don’t wait until after the next election – when you might be powerless to do anything about it.”

In a Q&A afterwards, Sir Ed argued that it was not necessary to hold a referendum on changing the voting system because “Labour’s manifesto talked about resetting politics, and this is a way to reset politics”.

He said that the Conservatives “had changed the electoral system in a number of places without asking anybody” – a likely reference to the introduction of FPTP elections for mayors and police and crime commissioners, something Labour recently reversed in Greater Manchester.

The Liberal Democrats and their predecessor Liberal Party have been campaigning for PR for more than 100 years.

In 2011, voters overwhelmingly rejected changing the voting system in a referendum, which had been secured by the Liberal Democrats when they were in coalition with David Cameron’s Conservatives.

Sir Ed – who was a member of that government – was quick to point out at the IfG event that the 2011 referendum was about changing to the Alternative Vote system, which he said was “absolutely not” PR.

Burnham became a convert to PR after being elected as Greater Manchester mayor under the Supplementary Vote system, which although not fully proportional did mean, he said, that he had to make an effort to “knock on every door” and convince Green and Lib Dem voters to back him with their second vote.