Trump ‘war games’ pledge and Tory Brexit ‘concessions’ talks

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Mr Trump’s announcement on so-called “war games” is seen as a large concession to Mr Kim, who – according to North Korean state media – has accepted an invitation to visit the US. Mr Trump, who called Mr Kim a “funny guy”, has also been asked to come to Pyongyang.

The biggest issue on the table – the denuclearisation of the Korean peninsula – was also discussed, with Mr Kim confirming his “unwavering commitment” to it. Whatever happens, writes BBC North America reporter Anthony Zurcher, the summit – with all its odd moments – shows that US and international politics “have been turned upside down”.

Theresa May averted a Commons rebellion over plans to give MPs a “meaningful” say over a final Brexit deal with the EU. Now Conservative MPs are to discuss in further detail what their role will be if no agreement is reached with Brussels by December. Some MPs say they were offered real “input”, in a last-minute concession ahead of a key vote on the EU Withdrawal Bill.

But Solicitor General Robert Buckland argued that allowing Parliament to “instruct” the government on what to do in the event of no deal would leave the UK in “very rocky constitutional territory”. BBC political editor Laura Kuenssberg says there have been “very, very dark mutterings” from those who were “persuaded by what they thought was a promise”.

Petrol prices have been rising almost daily since the end of April, despite wholesale costs falling, the RAC has claimed. It’s calling for retailers to cut prices for motorists by 2p a litre, arguing there is “no good reason” for the increases. But the Petrol Retailers Association said volatility in the value of the dollar and wholesale costs had added to pressures on independent fuel stations. The BBC’s Reality Check looks at why petrol prices vary so much.

By Dr Helen McCarthy, Queen Mary University of London

It is something that more than four million Britons now do on a regular basis and a way of working often associated with flexible lifestyles and greater freedom. Although men are more likely to work from home, four out of 10 homeworkers with an employer are women, a proportion that has grown in recent years. But for some women, the reality of balancing work with an unequal share of domestic duties can mean working at home falls short of expectations.

Theresa May’s aversion of a Commons defeat over Brexit is described by the i as a “win” for the prime minister, while the Daily Express warns that “tricky votes” still lie ahead. And the Financial Times says concessions to rebel Tory MPs have “all but ruled out Britain crashing out of the EU without an exit deal”. Meanwhile, the Sun reports on different interpretations among pro-Leave and pro-Remain Conservatives of what was actually offered, offering the headline: “May the farce be with you”. The Times focuses on the Trump-Kim summit, saying the US president has offered North Korea’s leader “the path to peace”.

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09:30 The Office for National Statistics releases its UK inflation figures for May.

13:00 England’s men’s cricket team, still smarting from a defeat by Scotland at the weekend, take on Australia in the first of five one-day internationals.

1991 Boris Yeltsin wins Russia’s first democratic presidential election.