On 7 May, Britain is widely expected to elect a hung parliament. This article offers a plausible scenario for the result, and a more speculative but optimistic scenario for what could follow. It is based on the polls and on recent political pledges, as well as on precedent from the 1920s. It illustrates the dilemmas that may be awaiting Britain in just two weeks.

When the results are in, the Conservatives have lost seats but remain the largest single party in votes and seats. Labour makes gains in England and Wales, but sustains huge losses to the Scottish National party north of the border. The SNP commands almost all Scottish seats. The Liberal Democrats lose half their MPs but the other half hold on. Ukip gets lots of votes, but only a tiny handful of seats. Nothing much changes in Northern Ireland, or for the Greens or Plaid Cymru.

David Cameron remains prime minister. A deal with Labour or the SNP is ruled out. By a whisker, the Lib Dems, Ukip and the Irish have enough MPs between them to guarantee him a majority. Under pressure from his right wing and the press, Cameron forms a minority government, tries to cut deals with the minor parties and decides to face the House of Commons in a vote on the Queen’s Speech, with a referendum on EU membership as its centrepiece.

The SNP cannot risk going into the 2016 Holyrood elections as the party that brought Labour down

But Cameron narrowly loses the Commons vote. The SNP is already committed to vote against. Labour, deeply aware of the way the SNP would exploit any other course of action on the vote in the 2016 Holyrood elections, votes against him, too. So do a handful of other MPs. Crucially, most Lib Dems abstain. The Cameron government falls. By now, the maths suggests that Ed Miliband could form a minority Labour government in its place. The Tories and the press are incandescent at the prospect but, under the terms of the fixed-term parliament act, Miliband seizes his chance. No deals are offered to any other party. In the vote on Labour’s Queen’s Speech, only the Tories and Ukip vote against. The SNP supports the new government, as do most of the minor parties. The Lib Dems remain divided. It is mid-June, and Britain has a Labour government.

So far, so dramatic. But also, so fairly predictable. Something fairly similar happened in 1923-24, leading to the first Labour government. But this, though, is where things get even more interesting. The practical question now is how long this Labour government could survive and what it could achieve. The answer is: not long, and not much. The prospects are formidably difficult.

The combination of arithmetic and politics means Labour would have few useful or reliable allies. And, as Jonathan Freedland argued last week, the challenges to the Miliband government’s legitimacy would be immense. Miliband would be excoriated by the press as the man who stole Downing Street. Even by recent standards, politics would be the object of contempt. In England, anti-SNP feeling would approach boiling point. Ukip would surge in the polls.

So what should Miliband do? One answer, which much of his party would support, is simply to battle on. Some Labour measures would pass. Others would fall or be amended. The government would get some things done. In spite of press hysteria about Miliband being in Scotland’s pocket, the reality would be the opposite. The SNP could exert little influence over Labour, because the SNP cannot risk going into the 2016 Holyrood elections as the party that brought Labour down.

Miliband’s ratings are, meanwhile, making François Hollande look like Europe’s most popular socialist leader. Two-thirds of Britons oppose the Labour government from the start. It begins to dawn on the Labour party that it must do something dramatic to staunch the rapid haemorrhaging of legitimacy and authority.

Miliband, therefore, makes what he calls “a big, open and comprehensive offer” to the Conservatives, which goes as follows.

“Much of my party is going to hate this,” he admits to Cameron, “and most of yours will loathe it, too. But the proposal is a pact, to last until Christmas, to achieve two things. First, we should abolish the fixed-term parliament act. And, second, we must introduce electoral reform for Westminster. Then, in the spring, we have a fresh election.

“I am open to some discussion on the nature of that reform,” Miliband says to Cameron. “It could be based on the alternative vote system that you sank in 2011, foolishly as I suspect you now realise in retrospect. Or it could be a multi-member constituency proportional system. But it must be one thing or the other and we must do it together.

“The goal is urgent and overriding. It is to give legitimacy back to parliamentary politics by allowing the different geographical and ideological divisions in Britain a much fairer representation at Westminster than we got in May. Without this, we are both going nowhere. We need a new start.

“There are advantages here for both of us. In Scotland, the nationalists will no longer be able to capture almost every seat. Instead, our parties and others will get a fairer showing from Scotland at Westminster. The SNP can no longer hold British politics by the throat with under 50% support in Scotland. In time, this will help to bring the Union – which is clearly still what most people want in both Scotland and England – back together, not before time. There are many other changes that we should make, but this one holds the key. Notice, too, that by ending the first-past-the-post system, we can put a dagger in the heart of the tactical voting on which the Lib Dems rely to our joint cost.

“There will be a cost for both of us,” Miliband continues. “Neither of our parties is likely to be able to form a majority government in the foreseeable future under this change. We will have to form coalitions. But how different is that from where we are now? The two-party dominance of parliament is an unsustainable myth. It no longer fits the mood and the nature of the country we have become. So be it.

“It is also likely that we will face stronger challenges under this system from an anti-immigrant party on the right and an anti-capitalist party on the left, as well as from Greens and regional parties. So be that, too.

“I am not afraid of the challenge. As I have always said, I am a conviction politician. Are you with me?”