Vince Cable today calls for a "progressive majority" of Labour and Liberal Democrat voters to join together and say yes to the alternative vote to prevent the next century being like the last one and "dominated by Tory governments".

In a marked escalation of Lib Dem language about their coalition partners in the runup to the AV referendum on 5 May, and talking for the first time about the effect a yes vote could have on the next general election, the business secretary explicitly raises the prospect of an anti-Conservative coalition victory in an effort to boost the Yes to AV campaign and shore up Lib Dem support in the local elections.

Cable says the moment has come to end the dynamic in which votes for Labour, the Lib Dems and Greens are split. Appealing to Labour voters more clearly than any of his Lib Dem colleagues, he says the "progressive majority" accounts for 50% of the electorate but their votes are shared between the three parties, which has allowed the Tories to win overall majorities on a minority of the vote.

If the supporters of all three parties can be persuaded to vote yes in the referendum the next election would be run under AV, and supporters of one party could vote for the others as second and third preferences, the business secretary points out.

In his interview, Cable – who hit out in the strongest terms yet against the Tories for attacks on Nick Clegg during the campaign – says: "It's been largely forgotten that Liberal and Labour MPs voted AV through the House of Commons but in 1931 the reform was never completed. Conservative governments have dominated ever since without securing a majority of the popular vote. It's time for the progressive majority in the country to rise above this narrow tribalism and support this reform because we need to make sure the progressive majority wins elections in this century and not the Conservatives as they did, by the back door, for two-thirds of the last century."

Cable's intervention marks a hardening of Lib Dem language in the last weekend before the royal wedding, when they fear people will have switched off. During the campaign so far, Lib Dems have refrained from pointing out how their coalition partners would fare in an AV system but the Tories have not held back from charging that their supporters should vote down the reform to punish the Lib Dems, launching personal attacks on Clegg.

The intervention comes after a week in which David Cameron hit the road for a no vote and dismissed accusations he had reneged on a deal with the deputy prime minister that he would take a back seat in the debate. Lib Dems have also been struck that Cameron appears to take no responsibility for the attacks on Clegg.

He undermined Clegg further by saying he defended the allocation of internship placements to the children of friends and colleagues, undermining one of Clegg's policies for improving social mobility.

Cable says he does not believe the prime minister's excuse that the no campaign is independent from him. He says a no campaign leaflet came through his own letterbox encouraging people to punish Clegg for "breaking promises" in government. It is promoted by William Norton, a Tory councillor in Redditch, Worcestershire. "AV leads to broken promises," it reads. "Nick Clegg is unpopular because he broke his promises: job cuts, VAT increase, tuition fees, public spending cuts. That's why he's pushing for AV to save his party."

Cable said: "I was surprised and alarmed to see a leaflet from the No to AV campaign put through my door with a brutal personal attack on Nick Clegg for his having loyally supported coalition policies including difficult public spending cuts. The claims that he promised not to embark on tough economic policies are simply false. I find it difficult to reconcile this leaflet attacking coalition economic policy with the fact that Mr Cameron is personally leading the no campaign and the leaflet is produced by a leading Tory donor. He [Cameron] may not directly control what his supporters are up to. But he must make it clear that he doesn't condone and will endeavour to stop personal attacks on his deputy for loyally supporting coalition policy.

"To stand by and let this happen is dangerous and puts considerable strain on the coalition. I haven't really reacted to this spat. But that leaflet was absolutely dreadful. It does take it on to a different level." Senior Lib Dems believe a TNS poll published today gives them cause for hope after previous polls have suggested leads for the no campaign of as much as 16%. The new poll found that 34% of people oppose AV but 32% support it.

After breaking down voting intention by party, most analysts believe the support of Labour voters – nearly evenly split – will be crucial to whether the change to the voting system goes through.

Asked if things can be the same again after May, Cable said: "If normal is working in a professional and businesslike way to deliver an agreed agenda then we can, but that doesn't mean ideological alignment or an absence of policy disagreement and I am not into lovey-dovey stuff either."