There is little to laugh about in the epic ongoing shambles that is Brexit, but there were at least a couple of moments of mild levity during my visit to Westminster this week. As I navigated the House of Commons between meetings I happened to find myself briefly at the door of a committee room and face to face with a gathering of Jacob Rees-Mogg’s European Research Group, as they were assembling for the latest chapter of their stuttering bid to depose the prime minister.

I am not sure which of us was more surprised to see the other, and I declined to offer them any advice. As if that wasn’t enough, I almost literally bumped into Boris Johnson while on my way to meet the prime minister. I asked the former foreign secretary if he wanted me to pass on any message to Theresa May. He suggested telling the PM to “get it sorted”.

It was perhaps an unconscious admission from Mr Johnson that the whole Brexit fiasco, which he helped set in train, is largely un-sortable, at least on the current trajectory. However, the fact that the Tory hardliners have, thus far, failed to mount any actual challenge to a prime minister whose authority is more weakened than that of any other occupant of No 10 in modern times betrays the weakness of the case for the hard Brexit they advocate, or for the disastrous no-deal outcome some of them crave.

The truth is, as is now becoming steadily apparent, that there is almost certainly no Commons majority for May’s proposed deal – and there is most definitely no parliamentary backing for no-deal.

With Amber Rudd, the newest member of Mrs May’s cabinet, now making clear that she expects parliament to exercise its authority to explicitly reject and prevent a no-deal outcome, it badly undermines the PM’s strategy, which has been to present things as a stark choice between her deal and the cliff edge of no-deal.

That is an utterly false choice, and it is now, day by day, being exposed as such. We should not be presented with the option of frying pan or fire. What is needed is a workable, better alternative to the prime minister’s deal. And it is incumbent on all of us who oppose it to come up with something that can command majority support. And while there is not yet a finalised alternative to the prime minister’s plan, there is now an emerging cross-party consensus that can lead to a much better outcome, with broad agreement between the SNP, Labour, the Liberal Democrats, Plaid Cymru, the Greens – and, indeed, some Conservatives – that parliament must reject both the current proposal and a no-deal outcome.

Continued, permanent membership of both the single market and customs union is one such alternative proposal that could well command majority support in the Commons. That outcome is one that the Scottish government has been consistently proposing for two years now. And it is one that is likely to find favour in Brussels. EU leaders may say that they are not open to renegotiation – they can say little else ahead of Sunday’s special summit, assuming it happens – but remaining in the single market and customs union does not involve the same renegotiation from the status quo as the UK government’s approach has done.

My first preference, of course, along with that of my government and party, is for us to remain in the European Union, which is what the people of Scotland voted for overwhelmingly. That could still be achieved by a so-called people’s vote, which I have made clear the SNP would support if it came to be voted on in parliament – and any referendum would have to have a remain option for it to offer a meaningful choice. That may yet be the alternative that proves capable of commanding a majority in parliament, and the SNP would be part of it. And if it takes a general election to break the impasse and ensure a less damaging outcome to the one that we currently face, then that is something the SNP would be very ready to fight. We would go into any such campaign, unlike most other parties, as having had a completely coherent and consistent position on Brexit.

From a Scottish perspective, one thing above all else is clear amid the Brexit chaos – that is, the cost to Scotland of not being independent. Independent Ireland has had nothing but support from its EU counterparts; Scotland has been treated with nothing but contempt by the UK government. The Tory party, or at least those of them who even care, may not yet appreciate the long-term cost to the union of such behaviour, but it will become apparent when the people of Scotland come to vote again on their future.

• Nicola Sturgeon is Scotland’s first minister