Progressives have a great opportunity this year to help reshape British politics for the better. The importance of the AV referendum campaign, and the impression the public gains of Labour’s role in it, must not be underestimated.

Many colleagues are rightly angry that the government used a single piece of legislation to deliver the referendum – which Labour supported – with an arbitrary reduction in parliamentary seats and partisan gerrymandering, which we opposed. We also believe the Liberal Democrats made a bad mistake by insisting the referendum be held on the same day as the elections in Scotland and Wales and local elections in England, when Labour people will be working to maximise our vote and inflict as much damage on our opponents as possible.

Some Labour people – including natural progressives – are suddenly finding the prospect of giving Nick Clegg and the Liberal Democrat leadership a short-term kicking more attractive than grasping this historic opportunity to change the voting system. One senior Labour figure predicted to me confidently that if the referendum were lost, Clegg would be toppled and the government would fall with him. But to be seduced by this hope would be a terrible error for our party.

The politician with the most to gain from a No vote is David Cameron. It is no coincidence that Tory MPs are unanimous in their support for first past the post. They have the most to lose, progressives the most to gain.

There are both broad political and narrow party reasons why Labour and those on the centre-left should support the Yes campaign. Constitutional reform is in our DNA. It has only ever been Labour governments that have delivered it – from House of Lords reform and devolution to freedom of information and the Human Rights Act. Our place has been on the side of the public challenging convention and the status quo, not defending it. The previous government endorsed a referendum on AV and our 2010 election manifesto promised that ‘’to ensure that every MP is supported by a majority of their constituents voting at each election, we will hold a referendum on introducing the Alternative Vote for elections to the House of Commons.’ Gordon Brown, a genuine convert from first past the post, believed this to be important to increasing the legitimacy of individual MPs and helping restore public trust in the wake of the expenses saga. These considerations have not gone away and to resile from a reforming position now would be a mistake.

The Labour pollster Deborah Mattinson has been at pains to stress in recent briefings that the problem of public distrust towards politicians has not gone away. Both her polling and that of others also show that if Labour is perceived to be pro-reform in the referendum campaign, this position will boost our vote in the accompanying elections.

Labour’s own political interests are also clear. Every time polling organisations have asked voters over the past 20 years who their second preference would be, the results show that Labour would have benefited from AV. We would have had bigger majorities in every election between 1997 and 2005, and in 2010 – despite our low popularity and longevity – we would have won four more seats, while the Tories would have secured 26 fewer. This is because Liberal Democrat, Green and Scottish and Welsh nationalist voters prefer us to the Tories by a significant margin.

Some have claimed that the new landscape has changed all that and that Labour can no longer rely on attracting Liberal Democrat second preferences. But that is not supported by the evidence of current polling or real elections. They show Labour benefiting most from Liberal Democrat defections and a majority of those staying loyal to that party still preferring Labour to the Tories. Furthermore, the boundary changes and seat reductions will help the Tories and hurt Labour. So keeping first past the post delivers the Conservatives a double advantage and makes it harder to achieve a Labour government with a Commons majority.

AV would also allow those natural Labour supporters who have voted tactically in unwinnable seats to vote for us – knowing their vote will count – and thus boosting our national share and helping revitalise the party in those regions where we need to win back seats to form a government.

Ed Miliband has shown courage in leading from the front on a cause opposed by many of his own MPs. Progress, Compass, the left-of-centre thinktanks, newspapers and commentators are virtually unanimous in their support for a Yes vote. Moreover, while Operation Black Vote is on board, the BNP is campaigning for a No vote. Yes is the right place to be. So now the legislative wrangling is over, let’s get out and fight hard for Labour victories in May’s elections and for a better voting system that’s in both Labour and the country’s interests.

For more information, please visit the Labour Yes campaign