The leaders of the Labour and Conservative parties came through the door of No 10 together and stood side by side in front of the microphones in the spring sunshine.

"We have a brief joint statement to make," they said. "The election is over and the people have spoken. Neither of our parties has received a mandate to govern alone. The country nevertheless faces urgent economic and social challenges. This is no time for the uncertainties of minority government. Throughout the campaign we experienced the public's burning desire for a break with the politics of the past. We shall therefore form a government of national unity, with an agreed programme, to serve for a full parliament. We shall invite other party leaders to work with us to put the national interest first. We are all in this together. Thank you."

In all the many articles that have already been written – and all those that will soon be written – about the possibility of a hung parliament after the 2010 general election, one significant option seems perversely unexplored – the big one: a deal between the two largest parties. That's right, between the Conservatives and Labour. Merely to state this possibility is doubtless to invite derision, and worse. For many on both sides a Conservative-Labour deal is in every respect the politically unthinkable.

It is nevertheless worth asking and answering, calmly, one simple question: Why not? The question deserves to be taken seriously for three main reasons. The first is that British elections are becoming increasingly fragmented. Votes and seats are shared between more parties than before. No large party can today count on automatic 40%-plus support as both Labour and the Tories once did. Inter-party deals have become common in the devolved authorities and local government. The trend would become more pronounced under a reformed Westminster electoral system.

The second reason is that some of the ancient differences between the main parties have blurred. This is sometimes misrepresented as "the parties becoming all the same", which is untrue. Nevertheless, some of the extremes of the past have been abandoned and some of the differences of today are more nuanced and pragmatic. Like football fans, British political parties retain a tribal culture, but the parties, like the football clubs, have learned they must adapt or perish.

The third reason is that, on occasion, needs must. There are practical arguments why, in some circumstances, an arrangement between the biggest parties might be the most viable option. A government of this kind might also do a good job, and might even be popular, too. Opinion polls certainly suggest as much.

In other European countries, the two major parties have often done this in circumstances well short of outright national emergency. Germany has twice been governed by grand coalitions, including from 2005 to 2009, while three German Länder are governed in this way. Germany has not collapsed – rather the opposite. The Netherlands has been governed by a grand coalition since 2006 and Austria since 2007.

But in Britain? Even today, we reflexively assume that the Labour and Tory projects are irreconcilable. Both parties are themselves coalitions already. Labour, in particular, is sustained by an oppositional not a governmental ethos. Neither party leader could hope to deliver on a deal. Big beasts in both parties would wreck it. The extremes would be empowered to revolt. The parties could not be put back together. These are all very serious practical objections.

Except that coalitions of this sort have existed and in some respects succeeded before, here as elsewhere. The two major parties of left and right came together three times in the last century, governing for a total of nearly 14 years – more on some calculations. The first was the Liberal-Conservative coalition formed in 1915 at the height of the first world war; the second was the national government formed in the wake of the economic collapse of 1931; while the third was the coalition formed by Winston Churchill in 1940 under which the second world war was won.

Wartime is different, many will say – rightly, of course. But how different? The national government reminds us that coalitions are not peculiar to wartime. A more accurate reality is that grand coalitions of the two main parties are formed when there is a perception of national emergency, whether in war or peace, in which single-party administrations seem incapable of taking necessary actions on their own. This perception is heightened when, as in 1915 and 1931, the governing party is already in a minority, as would be the case in any hung parliament, too.

The only important question, therefore, is whether 2010 may be such an emergency moment. Looking at the economic prospects depicted in Gordon Brown's implausibly rosy new year message, this may seem alarmist. Looking at them in the cold light of day, after the loss of the Brown government's majority and through the prism of a hung parliament, however, it could seem very different.

With the economy struggling and the markets in panic as they grasped how hard it would be to govern without the necessary majority, the pressure for an effective government – a government with an assured majority committed to do necessary but unpopular things – would be very great, not least from the media. It seems innocent to assume that either Labour or the Tories would automatically turn first to the Liberal Democrats in those circumstances – or that the Lib Dems would necessarily deliver. The big parties could calculate that they would be better off in a marriage of convenience with a historic enemy they respected, from which they could withdraw with dignity when the moment was right, rather than to embark on a more permanent entanglement with a Lib Dem party which at bottom they each despise.

The more one looks at the evolutionary dynamics of British politics, the more serious the grand coalition option may one day become. Is a Labour-Conservative deal really unthinkable? Only until you start thinking about it.