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One of the central problems Boris Johnson’s Number 10 has right now is that the parliamentary press pack has concluded it cannot believe a word it is told. Development after development since Johnson became Prime Minister has been denied, only for it to turn out a few days later to be true. “They even lied to me about the f***ing dog,” says one veteran political journalist.

This erosion of trust – worse than anything since the New Labour spindoctor shenanigans around the Iraq War – means that when Number 10 genuinely needs to deny something, on the basis that it is not true, it is not believed. Any appeal to plausible deniability falls apart when hacks are convinced that they are being lied to, not just a little bit as usual, but on an epic scale.

It applies the other way round too. When the Johnson Number 10 has good news to tell, in an area such as progress on the Irish border backstop issue – more of this in a moment – then it isn’t likely to be believed on that either.

So it was earlier this week when Peter Foster, the respected Daily Telegraph Europe editor, published a story saying that Dominic Cummings, Johnson’s main adviser, had said the negotiation with the EU is a “sham” – a fake, designed to fool people, stall parliament, and get Britain out without a deal.

The reason this mattered so much is that the Foster report helped shape the fevered conversation leading up to the dramatic rebellion and effective expulsion of 21 Tory MPs trying to stop no deal. The line from critics of the government is that there are no British government proposals on the backstop, there is no movement in Dublin or the EU, and it’s all just a delaying ruse to get the country ever closer to departure day. One former Tory MP Margot James cited the Foster report as justifying her vote against the government on Tuesday evening.

I’m not going to get into saying that Peter Foster’s reporting was wrong. He is a brilliant journalist and he was clearly briefed on this basis by his sources. Multiple interpretations of the same event are often available from different sources who were in the same room. That’s politics. We’ll all need to wait for the release of official documents years down the line for historians to establish properly what happened in these crucial discussions.

But there is genuine fury on the government side about the Foster report. “Categorically, it is simply not true,” an official told me.

Why the anger? It landed just when there is some progress on the question of the Irish border backstop. This should have been big news, but quite a lot else was happening yesterday as the Tory party tore itself apart. Lost in the cacophony, the Prime Minister suggested yesterday that he is now prepared to accept an all Irish economy on agriculture and related sectors, applying EU rules.  In effect, checks would take place in the Irish Sea, or at ports on the coast. This would negate the need for the backstop.

This is far from a perfect solution, and various forms of it have been suggested before by critics of the government looking for a compromise and a way round Theresa May’s red-lines.

“This would deal with about 90% of the issues, in terms of checks required,” says a government source.

The Irish government – under some pressure domestically – is suspicious but it is listening. They would really rather avoid an accidental no deal via the EU flinging the UK out, or a situation in which Johnson wins a majority (not impossible) and then takes the UK straight out himself.

While the Irish government can’t back down entirely, this could form the basis of a compromise. Both governments would present it as them being custodians of the peace process. Northern Ireland would end up with yet more government spending and the most whizz-bang imaginable infrastructure at its ports.

This morning The Sun had a hint of what is going on in this regard, buried in a panel in the middle of its coverage of the chaos in the Commons.

“Under the plan, Northern Ireland would match Irish and EU rules in certain sectors after Brexit to avoid the need for a hard border. The idea emerged ahead of talks with Irish PM Leo Varadkar, left, next week.

It mimics a compromise European capitals were brainstorming — where the North  would mirror Brussels on animal and plant health. It threatens to enrage Ulster Unionists by, in effect, putting a  border down the Irish Sea between the Britain and Northern Ireland. But  senior DUP sources hinted they could back it,  as long as Belfast’s  Stormont Assembly  has a veto on which future EU rules Northern Ireland accepts.”

The DUP – which doesn’t want no deal either – is signalling that there is scope in this potential arrangement to find a way through, if Dublin agrees and tells the EU the Stormont safeguard is necessary.

This is not – I repeat not – a blithe declaration that the British government has discovered the secrets of alchemy, a magical Brexit solution that vanishes away all concerns.

A lot could go wrong in the next week or so. Everyone will deny everything and there will be a lot of shouting, most of it to no useful end. Ireland’s leaders might take fright and refuse to trade. Number 10 could fumble the ball. Hardline Tory Brexiteers and Nigel Farage’s team may say that this compromise on the backstop is insufficient or a betrayal and they won’t be happy with any form of Brexit that fails to include a declaration of war against Belgium.

But the game is afoot on the backstop.