The prime minister met the European Commission President during his visit to the United Nations General Assembly.
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Frost, wind and rain forecast as autumn warmth fades for many
Late summer warmth is set to break in many areas as rain and wind sweep in from the west.
Child ketamine users getting bladder damage describe 'peeing a jellyfish'
Doctors running the UK's first and only dedicated NHS clinic for children with ketamine bladder say they are seeing patients as young as 13.
Fresh bedsheets and dusk walks: Expert tips for sleep-deprived freshers
Why it's a good idea to get out for an evening stroll, and other essential sleep advice for students.
'Poison seller' who sold my daughter deadly drugs should rot in hell
Louise Nunn's daughter bought drugs from Canadian Kenneth Law, who sold toxic chemicals online.
'I don't have a buoyancy aid': Living without the Bank of Mum and Dad
Three 20-somethings tell BBC News how they are navigating life without parental support.
Europe's car makers are in crisis. Will the threat of war rescue them?
Auto executives across Europe hope rearmament can help them flex their industrial muscles once more.
IMF tells advanced economies to 'bring debt down' as borrowing costs rise
In an interview with the BBC, Kristalina Georgieva says economic shocks had pushed "debt levels up like a staircase not to heaven".
Rare look at the remote engine rooms powering China's AI ambitions
The BBC is in Inner Mongolia where dozen of Chinese data centres are being constructed, as the country aims to lead the world in artificial intelligence.
Trump threatens to 'annihilate' Iran in UN speech as officials meet on sidelines
In his speech, the US president pondered whether a peace deal would be agreed or whether he would have to take extreme action against Iran.
US to build two military bases in Greenland under new deal with Denmark
The defence deal signed at the UN General Assembly also re-affirms Denmark's sovereignty over its semi-autonomous Arctic territory.
Trump says he can do business with Burnham but criticises 'terrible' Chagos deal
The UK has proposed handing the Chagos Islands to Mauritius and paying to lease back an important military base.
Plot targeting Manchester's Jewish community disrupted, say police
Two men were arrested in Manchester on Sunday, say counter-terror police.
Earl Spencer should pull Diana book from shelves, Piers Morgan says
Princess Diana's brother apologised to Morgan for a factual error in his memoir. Morgan said he is "pursuing legal action" against Spencer.
American power, AI and a walkout - key moments from Trump's UN speech
BBC correspondents who covered the president's address on Tuesday assess five key moments.
Lib Dems leave conference buoyed by Davey's message
Concerns over Sir Ed Davey's leadership were dampened by pledges at conference and his performance.
Lib Dems leave conference buoyed by Davey's message
Concerns over Sir Ed Davey's leadership were dampened by pledges at conference and his performance.
Watch: Burnham 'gets it' says Trump, as the two leaders meet for first time
Donald Trump says he can do business with Andy Burnham at their first face-to-face meeting in New York, but criticises the "terrible" Chagos deal.
Jacks stars as England grind out win over Sri Lanka
Will Jacks' all-round efforts help England grind out an 89-run victory over Sri Lanka in the first one-day international at Chester-le-Street.
Ukraine anger as EU removes Russian oligarchs from sanctions list
Alisher Usmanov and Mikhail Fridman both have close ties to President Putin, and Kyiv said the move sent Moscow the wrong signals.
Booker Prize judges reveal shortlisted novels after selection 'tussle'
Past Booker winners Marlon James and Douglas Stuart are among the nominees for this year's award.