The main electoral impact of the Liberal Democrats in modern times has been to help deny the Conservatives a working Commons majority.  They have done so regardless of whether the latter have been in government or opposition.

In 1974, the Conservatives were in government, the Liberal vote surged, Edward Heath failed to win a majority and Jeremy Thorpe refused to enter a coalition with him.  In 2010, the Tories were in opposition, the LibDem vote rose slightly, David Cameron failed to gain a majority – and Nick Clegg took his party into coalition.

It is significant that sweeping LibDem gains haven’t tended to harm Labour.  In 1997, the party gained 25 seats, taking its total to 34.  In the same election, Tony Blair won a landslide.  He and Paddy Ashdown had crushed the Conservatives in a pincer movement.

The tumultuous effects of Brexit have resuscitated the LibDems and are reviving their prospects.  Coalition nearly killed them, at least at Westminster.  But the EU referendum has given them a new lease of life.  Once again, it is most evident in areas which otherwise return Conservative MPs or councils.

Out of their 14 MPs in England and Wales, all those elected as Liberal Democrats in 2017 had the Tories in second place.  In the local elections last spring, all their councils gained were in yellow/blue areas.  Their revival tends to be concentrated in areas in which they flourished between roughly the late Thatcher and late Cameron eras.

This is the context in which to viewed their latest shift on Brexit, the opportunities it is bringing them, and the defections it is gaining them.  The shift to revocation takes place in the context of their competiton with Labour.  The more red votes the party can squeeze in blue/yellow marginals, the more seats it is likely to win.

So as Labour gradually commits itself more explicitly to Remain, to be delivered through the medium of a second referendum, the more the LibDems must try to outflank it.  Junking the referendum and going straight for revocation is the obvious means of doing so.

The ploy carries risks for Jo Swinson’s party.  Revocation may play well in South-West London or university-type seats.  But it is hard to see how it will be a plus in Brexity South West of England.  Swinson seems to be going for broke in the Remain heartlands of 2016: the capital itself and what might loosely be called the greater South East.  Plus Scotland.

In her perfect world, the Liberal Democrats will sweep up London seats in which they have not been previously competitive.  Hence Chuka Umunna’s flight from Streatham towards the Cities of London and Westminster.  She may also be hoping to have a crack at Labour in some of its north London constituencies.  The prospect is agitating pro-EU Labour MPs such as Keir Starmer and Emily Thornberry to push harder for Remain.

It is tempting to write off the Revocation policy.  After all, Swinson can only implement it herself with the Commons majority that she won’t win.  That clip of a prosperous-looking LibDem audience whooping it up for Guy Verhofstadt’s imperalist ravings won’t impress Revocation-sceptic centrist voters.

But the shift will have an effect on the conversation at Westminster.  Were Swinson to win that mythical majority, Revocation would be one thing: she would have won the right to implement it, fair and square.  But the policy will be quite another if Brexit doesn’t take place on October 31, and MPs begin to drift in its direction without a mandate.

That would be to flick a V-sign not only at 17 million Leave voters but the entire EU referendum result – with consequences for the stability of our already shaken politics that are potentially shattering.  Revocation in that context would be the real extremism, not No Deal, for which at least there is a mandate if necessary.

Swinson’s gambit may blow up.  It could just be that LibDem support in blue/red marginals collapses, handing the Conservatives new seats in the Midlands and North, and that these outnumber LibDem gains in the blue/yellow marginals.  Or that the Luciana Berger and Angela Smith defections to the party are the start of something bigger

Four-way politics in England and Wales complicates all these calculations, as does its equivalent north of the border: Swinson herself could lose her seat to the SNP, which took it from her 2015, before she won it back two years later.  Which reminds us that there will be more to any forthcoming general election than Brexit.

This should lead us to look at the LibDems in the round, as their conference continues today.  Coalition sobered them up, at least for a while, and provided some good Ministers: Steve Webb’s work with Iain Duncan Smith at Work and Pensions stands out.

But most of the stars of that era have either left the Commons or are leaving: Clegg, Webb, David Laws, Vince Cable.  Their successors look less impressive.  And the Tory defectors, Phillip Lee and Sam Gyimah, may not be in the Commons for much longer (and nor may the Labour ones, come to think of it.)

The LibDems have a core problem that they cannot shake off.  In local government, they may well revive further.  In the European elections, they can build on their second place won this year. In Scotland, they could conceivably govern as part of some rainbow coalition.  That is also possible in Wales, where they are currently weak.  Westminster is a different proposition.

For a lesson of the Cameron years is that first past the post sets the party up for punishment if it goes into coalition.  Doing so tends to have the effect of depressing smaller parties in any event, as Paddy Ashdown used to point out, regardless of the electoral system in question. But first past the post intensifies the effect.

Were the LibDems to go into coalition with the Conservatives again, their lefter-leaning voters would desert them.  The reverse would be true were they to go into coalition with Labour.  (The Lib/Lab pact scarcely helped the Liberals in 1979.)  In any event, a lot of LibDem support comes from protest voters.  In 2015, many of these decamped to UKIP, in defiance of any ideological consistency.

This suggests that the most durable option for the LibDems in any future hung Parliament would be confidence and supply.  It is almost impossible to imagine Swinson going into coalition with Jerermy Corbyn or Boris Johnson in any case.

No Ministerial cars; no red boxes.  No more posts as Deputy Prime Minister, or LibDem Ministers shaping government policy.  It is a grim fate for any ambitious politician to accept, but the LibDem mentality is different to that of Labour, as well as us Conservatives.  They are used to marginality, being squeezed – and the joys of irresponsible opposition. Brexit has changed much for them, but less than one might think.