Glancing at the headlines is my old-fashioned start to the day. As Labour apparently weigh in behind a people’s vote, two contrasting verdicts catch the Brexit-bloodshot eye this morning.

The Labour-strutting Daily Mirror sets an upbeat tone with: “Corbyn backs second Brexit vote”, while the Leave-loon Daily Express goes with: “Our final say on Brexit was June 23 2016!”

These papers may shout at each other from different ends of the room, but they both belong to Reach, the publishing company formerly known as Trinity Mirror. In this arrangement, they reflect family members who disagree over the disagreeable thing.

Yesterday, Reach warned about the impact of Brexit on advertising while reducing the estimated value of its newspaper business by £200m. On one level, this is just another gloomy story about the decline in print sales. On another, it suggests that one of its newspapers blindly backs something its owner believes could be bad for business.

Reach bought the Express group and, as part of the deal, inherited crusty readers whose crusted views were opposite to those of Mirror readers. Maintaining a duality of opinion for two opposing sets of readers is encouraging in a sense, even if the devotion of the Express to Theresa May’s endless outing of no hope does seem barmy.

Is a second vote a good idea? I’ve been conflicted about this for a while. Considering the poor level of debate for the first one, and the shocking lack of any plan for what would happen if we voted to leave the EU, a second referendum would at least be better informed – that’s if everyone hasn’t stopped listening long ago.

But here’s the problem: if you don’t like referendums, how does it make sense to settle matters by having another referendum? That’s where I stumble over this one. I’d willingly vote to stay in the EU again. But that doesn’t remove the awkward fact that we’ve voted once already and, by a squeak, said we wanted to leave.

The Guardian’s take on this morning’s story is: “Corbyn: We’ll back a public vote to stop Tory Brexit.”

That label is a good one, in a sense, for Brexit is mostly a Tory obsession with its roots in ancient blood feuds and Tory psychodramas. But this leaves open the question of what a Labour Brexit would look like. There’s a horrid portmanteau word for that, too – Lexit, the left-wing case for Brexit. Followers will tell you that the EU is a neoliberal plot or something. I’m with the writer and comedian David Baddiel who tweeted a while back – and I’m not putting in those prissy stars favoured by some newspapers – “I’ll be honest with you. I have no fucking idea what neo-liberalism is.”

Baddiel could have Googled the following meaning: “A modified form of liberalism tending to favour free-market capitalism.” But his point, I guess, was that certain people splutter the word like an anti-spell or something.

Jeremy Corbyn is almost certainly a Lexit lover at heart, as he’s never favoured Europe; but that love cannot speak its name right now, hence the ducking and diving. He also hates neoliberalism, whatever it is, as embraced by his predecessors, Blair and Brown.

The weird thing about seeing Europe as a neoliberal confidence trick is that if we leave Europe, we will be more fully exposed to neoliberalism as brandished by the US and loved by Trump.

So, in terms of neoliberalism, whatever it is, we’d suffer even more of it than if we stayed in Europe. Brexit all round, really: a surprise pudding where the surprise is never nice.