Britain faces a constitutional crisis, according to many, including at least one cabinet minister. But is it a crisis simply because the rules regulating parliament make life difficult for the government?

A conflict between government and parliament is almost inevitable when, as with Brexit, the government cannot command a majority of votes in the Commons. But there is a deeper crisis within parliament itself. MPs have put the European Union (Withdrawal) Act on the statute book, which entails us leaving the EU on 29 March, in just eight days’ time.

But they have rejected every proposal to make Brexit a reality. They have twice rejected the deal; and they have also three times voted against amendments proposing that Britain remain in the customs union or the internal market.

Last week MPs also rejected a no-deal Brexit, while an absolute majority of MPs rejected a “people’s vote” by 334 votes to 85. Without a further referendum, it is hardly possible for MPs to revoke article 50 and reverse Brexit. In addition, on 16 January MPs decided not to replace the government which is steering the Brexit process, when they rejected a motion of no confidence that could have precipitated a general election.

In the classic Marx brothers film Horse Feathers, Groucho, playing Professor Wagstaff, tells his fellow academics: “I don’t know what they have to say, it makes no difference anyway. Whatever it is, I’m against it.”

It is illogical for MPs to keep the government in office while rejecting its flagship policy. Before the Fixed-term Parliaments Act, it would have been impossible. The government would have had to make the vote on the deal a matter of confidence. MPs would either have had to accept it, or the government would have had to resign. But under the act the government can only be made to resign after a specific vote of no confidence not attached to other legislation.

MPs have willed Brexit without willing the means to secure it. They have left the country, in the words of Bill Cash, Conservative chair of the European scrutiny committee and rabid Brexiteer, “at a dangerous crossroads in the middle of a fog”. The best course in such a situation is simply to wait until the fog clears. But that option is not available. If MPs do nothing, Britain will leave the EU next week without a deal, so exposing the country to the full panoply of EU tariffs and regulations as well as a hard border in Ireland.

MPs have put Theresa May in the difficult and perhaps humiliating position of seeking an extension to the Brexit date from Brussels. That requires the unanimous consent of the other 27 member states. They may well agree the short extension she requested today, until 30 June. But they will expect, in the words of Donald Tusk, president of the European council, “a credible justification for a possible extension and its duration”. For, as France’s Europe minister, Nathalie Loiseau has said, an extension is a method, not a solution. The 27 will need a clear indication from the government both on the process to be followed and the proposed outcome.

Elections at the end of May could see Nigel Farage return to the European parliament. Photograph: Patrick Seeger/EPA

Presumably the fact that MPs could not make up their minds would not seem a “credible justification”. A short extension leaves no time for parliament to reconsider alternative models, already rejected – such as remaining permanently in the customs union, as proposed by Labour, or the Norway option, which has been put forward by a number of MPs. It is in any case doubtful if either could command a majority. They would certainly not command a majority among Conservatives.

Remaining in the customs union would prevent Britain pursuing an independent trade policy; and for many Conservatives that was the whole point of Brexit. Theresa May’s deal does in fact secure most of the advantages of the customs union without its obligations.

Remaining in the internal market entails freedom of movement, which most Conservative MPs, and indeed most Brexit voters, reject. It is in any case rather late for MPs to consider mobilising behind an alternative. They have had two years to do that. It is also a bit late for MPs to object to the Northern Ireland backstop, which was first agreed by the government in December 2017.

Any extension beyond 30 June, which May says she opposes, would require Britain to take part in the European parliament elections at the end of May. The EU charter of fundamental rights gives every EU citizen the right to vote and stand in these elections, to ensure that “citizens are directly represented”. If that right is abrogated, the government could expect to be challenged in the courts. And EU leaders would not relish allowing Britain to take part in elections that would almost certainly result in Nigel Farage and his fellow Brexiteers being returned to the European parliament, and which would allow Britain to take part in EU budget negotiations and the appointment of a new commission.

The choice, therefore, remains stark. Either the Commons votes for Theresa May’s deal, or Britain leaves without a deal. The Speaker has indicated he may judge a further vote on the deal to be out of order. That, however, need not be an insuperable barrier. The convention that he has cited can be overridden by a Commons motion to reconsider the deal “notwithstanding” the convention. If MPs come to favour the deal, they can probably summon up a majority to pass such a motion.

Margaret Thatcher once declared: there is no alternative. MPs seeking to peer through the fog that Bill Cash has identified may well come to feel the same is true today. There is now, so it seems, ultimately no alternative to May’s deal.

• Vernon Bogdanor is professor of government at King’s College London and author of Beyond Brexit