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Jean-Claude Juncker insisted he is still 'optimistic' for a Brexit deal today as he met Boris Johnson for crunch talks.
The EU commission president smiled and waved as he arrived at the restaurant in Luxembourg accompanied by chief negotiator Michel Barnier.
'I am always optimistic,' he told reporters. 'Europe never loses patience.'
Mr Juncker and Mr Johnson shook hands before going inside the restaurant, where they are due to consider the impasse over a lunch of snails, salmon and cheese.
Earlier, Mr Johnson insisted he is 'passionate' about getting a deal and hailed 'signs of movement'.
But he said he would 'get Brexit done' by ensuring the UK leaves by October 31, whether or not an agreement is reached.
Mr Juncker has played down the prospects of a breakthrough today and warned that 'time is running out'.
The talks are a pivotal moment in the Brexit process, with just 45 days left until the UK is due to leave.
Mr Johnson has made clear he will reiterate his determination to stick to the deadline, whether there is an agreement or not - likening himself to the 'Incredible Hulk' breaking free of 'manacles'.
The government has ramped up efforts to get a settlement with Brussels after Remainer MPs moved to hem in the government by ruling out No Deal, and blocking an election.
Legislation passed by Parliament obliges the PM to seek an extension if an agreement is not struck by October 19 - the day after a make-or-break EU summit concludes.
However, allies of the premier have been claiming there is a loophole in the rebel law that could allow the government to ignore it.
Jean-Claude Juncker (left) and Boris Johnson (right) leaders shook hands before going inside the restaurant in Luxembourg today, where they are due to consider the impasse over a lunch of snails, salmon and cheese
EU commission president Jean-Claude Juncker (left) smiled and waved as he arrived at the restaurant in Luxembourg with Michel Barnier
The leaders are meeting at the Le Bouquet Garni restaurant in Luxembourg today - rather than at an EU commission or a UK venue
One of the place settings in the restaurant today ahead of the lunch discussions
Mr Johnson and Mr Juncker shook hands again for the cameras inside the restaurant today
Mr Johnson will meet Mr Juncker at lunchtime – their first encounter since he entered Downing Street.
Over a meal of snails, salmon and cheese, he is expected to tell the former Luxembourg prime minister that he will reject the offer of any further extension, even if it is just for a few days.
In the video posted on Twitter today, and filmed on board his plane on Friday, Mr Johnson was bullish about his chances.
As the aircraft rose into the the air, Mr Johnson compared it to the UK taking off under his leadership.
He said he was 'cautiously optimistic' about reaching an agreement with Brussels, but added: 'We are going to get it done. We are going to come out of the EU on October 31.'
He also again rejected anger about his decision to suspend Parliament until October 14 - which has been controversially ruled illegal by Scottish judges.
Pointing out that the Commons was only sitting for four days fewer than previously expected, Mr Johnson said there would be plenty of time for debate, adding: 'They have had three years to talk about what to do about Brexit.'
A No10 source said: 'He could not be clearer that he will not countenance any more delays, we will be leaving on October 31 – no ifs, no buts.
'Any further extension would be a huge mistake. It is not just a question of the extra dither and delay – it is also the additional long months of rancour and division, and all at huge expense.
Here is how the coming weeks could pan out:
Today: Boris Johson meets Jean-Claude Juncker for lunch in Luxembourg.
September 17: Supreme Court hears case on whether prorogation of Parliament was illegal.
September 21-25: Labour conference in Brighton
September 29-October 2: Tory conference takes place in Manchester, with Mr Johnson giving his first keynote speech as leader on the final day. This will be a crucial waypointer on how Brexit talks are going.
October 14: Unless it has already been recalled following the court battle, Parliament is due to return with the Queen's Speech - the day before Mr Johnson had hoped to hold a snap election.
October 17-18: A crunch EU summit in Brussels, where Mr Johnson has vowed he will try to get a Brexit deal despite Remainers 'wrecking' his negotiating position.
October 19: If there is no Brexit deal by this date Remainer legislation obliges the PM to beg the EU for an extension to avoid No Deal.
October 21: Decisive votes on the Queen's Speech, which could pave the way for a confidence vote.
October 31: The current deadline for the UK to leave the EU.
November/December: An election looks inevitable, but Labour is hinting it might push the date back towards Christmas to humiliate the PM.
'We must finally deliver on the 2016 referendum. This is why the PM will stress to Mr Juncker that, while he wants to secure a deal, if no deal can be agreed by October 18 his policy is to leave without a deal on October 31 – and reject any delay offered by the EU.'
Writing in the Telegraph today, Mr Johnson said the UK was working 'flat out' for a deal, despite the EU complaining that no formal proposals have been put forward yet.
'I believe passionately that we can do it, and I believe that such an agreement is in the interests not just of the UK but also of our European friends,' the PM wrote.
'We have all spent too long on this question. And if we can get that deal, then of course there will be time for Parliament to scrutinise and approve it before the end of October.'
'But be in