Not unreasonably, all political commentators are presently focusing on the parliamentary imbroglio around the Brexit vote (or perhaps votes) and the Conservative leadership. But there’s another elephant in the chamber that could blow the present structure of British politics to smithereens.

Assume that the House of Commons throws out Theresa May’s Brexit deal, and that Labour then tables a no-confidence vote. Both scenarios are highly likely. Assume, then, that a no-confidence vote in the prime minister succeeds (less likely, but possible – particularly after the recent volte-face by the DUP). What happens next?

Under the Fixed-term Parliaments Act of 2011, there has to be a general election unless an alternative administration obtains a vote of confidence within a fortnight. Suppose Jeremy Corbyn fails to obtain one – highly likely so long as it is understood that there is another option. Buckingham Palace then has to ask somebody else to form a government. But whom?

No single other party could form a viable administration, but there is a hidden party which could. It consists of the vast majority of MPs who would seek to avoid, at all costs, the economic disaster of a hard Brexit and would support a second referendum now that the facts are known, as David Davis and Jacob Rees-Mogg used to advocate when they found it convenient to do so.

The Queen has the prerogative power to choose whom to invite to form a government. Indeed, before the Conservatives had a leadership election system, the Queen was used by that party to settle its internal rivalries (most recently, following the resignations of Eden and Macmillan). But, in modern times, the palace is deeply reluctant to intervene; as it told No 10 after the inconclusive 2010 general election: “Please keep the cameras at your end of The Mall.”

In this situation, however, the palace would have no alternative but to intervene, in order that the Queen’s government could be carried on. So it would summon potential leaders of a “coalition of the willing”, or the famous “Government of All the Talents”, consisting of the silent Commons majority which prefers a second referendum to a hard Brexit. Let’s say: Dominic Grieve, Sir Keir Starmer, Sir Vince Cable and Ian Blackford.

The Queen would then invite them to select a potential prime minister, who could either accept on the spot and kiss hands on appointment, or – more probably, as with Sir Alec Douglas-Home in 1963 – say that he’ll go away, try and then report back. It is a beautiful irony that the invitee would then become a formateur in accordance with mainland European practice.

As I discovered in the run up to the 1997 general election, when I was Paddy Ashdown’s technical and legal adviser on coalitions and hung parliaments, the Queen’s private secretary is (or was then) pretty cute at contingency planning (four of us met him for talks that lasted just 45 minutes). It would be surprising if the present incumbent were not doing just this as I write.

The fledgling administration would then seek to achieve a majority for a confidence vote. Its platform on Brexit would be to pause Article 50, while it ran a second referendum on the choice between Remain and a hard Brexit. On the basis of previous statements, the EU would willingly grant a postponement for this purpose.

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But resolving the Brexit imbroglio in this way would not be the only prize. A coalition of the centre would have been created in government. It could then constitute itself as a new party. Once the European issue had been sorted, it could seek the authority of a general election to reshape British politics for a generation, rejecting both extremes, and based on a free market economy but not a free market society, combining responsible capitalism with social justice.

The electorate could then make a positive choice, rather than voting either Conservative or Labour because of the deficiencies of the other.

Crises beget opportunities. This is a big crisis, and an even bigger opportunity.