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A third way?
The BBC understands that Downing Street has come up with a third model for the customs union after Brexit - after ministers failed to agree on either of the first two put forward. The intractable problem of customs is central to the future of trade and a significant part of finding a solution to the Irish border problem. It's even prompted physical acts of destruction from at least one minister.
We don't yet know the details of this third model, but given that the other two - more on them here - seem to be politically or practically undeliverable, all hopes will be riding on it. The whole cabinet gets together at the prime minister's country retreat, Chequers, on Friday to discuss it - and, Theresa May hopes, back it.
Last week, European Council President Donald Tusk issued a "last call" to the UK to agree a position if a Brexit deal is to be done by the October deadline. As BBC political editor Laura Kuenssberg puts it, if Mrs May can't end the fight this week- by picking a winning side or forcing a persuasive compromise - the EU may call time.
High Street suffering goes on
The UK High Street's woes are well-documented. BBC 5 Live's Wake Up To Money has been tracking shop closures and retail administrations, and the latest figures make for grim reading. Nearly 22,000 jobs have either been lost or are set to go this year alone. About 1,200 shops run by major chains have either shut or are at risk of closure. The BBC's Jon Kelly has looked closely at the death of just one, a Poundworld in Northumberland, and the lives that have been affected by it.
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Redrawing Mexico's political map
Left-wing candidate Andrés Manuel López Obrador is heading for a landslide victory in Mexico's presidential election. As our what-you-need-to-know guide explains, it's a political earthquake in a country where almost all voters alive have never known a leader who wasn't from either the Institutional Revolutionary Party or the conservative National Action Party. Sunday's election followed one of Mexico's deadliest campaigns in decades with more than 130 political candidates and party workers killed.
Mr López Obrador - find out more about him here - was the candidate most critical of Donald Trump and he has vowed to make the US president "see reason". As the results rolled in, Mr Trump tweeted his congratulations.
How green are festivals?
By Reality Check team
When people are rushing between headliners at festivals, the last thing on their minds might be how to recycle their food containers, or where they put their reusable cup. But, with more and more focus on going green, festivals across the UK are pledging to cut back on plastics, leftover waste and even glitter. So, what are the biggest environmental impacts of festivals and what's being done to combat them?
Read the full article
What the papers say
Another week, another crunch Brexit moment, and the topic once again dominates the papers. In the Daily Telegraph, backbencher Jacob Rees-Mogg warns Theresa May she will face an open Tory rebellion that risks the collapse of her government unless she delivers the Brexit "she herself has promised". The i says hardline Brexiteers like him have been told they will have to topple her to prevent any deal that keeps trade aligned with the EU. The Times speculates that on past form the PM's preference may be to seek refuge in fudge, but it feels clarity cannot be avoided forever. Elsewhere, both the Daily Mail and the Daily Mirror launch campaigns to "save the High Street". The former places much blame on "crippling" business rates, while the latter says a different vision altogether for our town centres, less focused on retail, may be needed.
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Split Cheryl and Liam go their separate ways
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15:30 Theresa May will make a statement in the Commons updating MPs on progress made at last week's EU leaders' summit
Today Wimbledon gets going with both Serena Williams Roger Federer in action
On this day
2001 Barry George is sentenced to life in prison for murdering TV presenter Jill Dando
Plastic-eating bacteria discovered by student could help solve global pollution crisis (Independent)
What Love Island really says about the world we live in (Herald Scotland)
What it costs to be smuggled across the US border (New York Times)
Do England really have an easy route to the World Cup final? (Sunday Mirror)