Donald Trump: US president meets Theresa May at Blenheim Palace

US President Donald Trump has been welcomed to Blenheim Palace by Theresa May, on the first day of his UK visit.

The black-tie dinner, with 150 invited guests, is expected to focus on post-Brexit trade, and comes days after Mr Trump said the UK was in "turmoil".

He and First Lady Melania Trump arrived in the UK on Thursday afternoon.

Protesters have gathered outside the US ambassador's residence in London, where the Trumps are staying tonight, and near Blenheim Palace.

Extra security is in place to police the protests, but Mr Trump has said that Britons "like me a lot" and that he feels "fine" about any such protests.

The Trumps left Winfield House at approximately 19:00 BST, with Mrs Trump wearing a full-length yellow dress with a pleated skirt.

Mr Trump, who will also spend time with the Queen during his two-day working visit, said earlier of the British public: "I think they agree with me on immigration... You see what's going on throughout the world with immigration... I think that's why Brexit happened."

He said "Brexit is Brexit" and the British people "voted to break it up, so I imagine that's what they'll do but maybe they're taking a different route - I don't know if that is what they voted for".

Mr Trump has recently been under fire for his own immigration policy, which resulted in the separation of immigrant families.

The Trumps landed at Stansted Airport, Essex, at 13:50 BST before a helicopter took them to Winfield House in Regent's Park, where they are staying as guests of the US ambassador.

He was met at the airport by dignitaries including International Trade Secretary Liam Fox and US ambassador Woody Johnson.

Speaking at the Nato summit in Brussels before he arrived, Mr Trump said the UK was a "hot spot right now".

His visit comes as the government publishes its plans for the UK's relations with the EU after Brexit.

Earlier this week Mr Trump said it was "up to the people" whether Mrs May stayed on as prime minister after two cabinet ministers resigned within hours over her Brexit policy.

A large police presence has been building up outside Blenheim Palace. Police officers estimated there were more than 1,000 people demonstrating before Mr Trump's arrival.

A group of protesters has also gathered outside a fenced-off area in Regent's Park, close to the entrance of Winfield House, where Mr Trump is staying.

Among those attending the black-tie dinner at the ancestral home of former Prime Minister Sir Winston Churchill are cabinet ministers and business leaders.

Guests are dining on Scottish salmon, Hereford beef fillet and strawberries with clotted cream ice-cream.

Only one person, the digital entrepreneur and philanthropist Baroness Martha Lane-Fox, has publicly refused the invitation.

Mrs May said the UK visit would be an opportunity to boost trade links and strengthen co-operation on security.

Along with trade and security ties, Downing Street said the other key areas to be discussed between the two leaders included Brexit and the Middle East.

Ahead of Mr Trump's visit, Mrs May said that when the UK leaves the European Union "there will be no alliance more important in the years ahead".

Mr Trump travelled to the UK from the Nato summit, where he said member countries have agreed to increase their military spending.

Mr Trump had joked earlier this week that his meeting with Vladimir Putin in the Finnish capital Helsinki on Monday "may be the easiest" part of his European trip.

Downing Street insisted Mrs May welcomed Mr Trump's decision to "engage" with the Russian leader.

But she also warned Mr Trump not to ignore the "malign behaviour" of Russia.

By James Landale, BBC diplomatic correspondent

Since Donald Trump took office, Theresa May has had to disagree with him publicly over his decision to impose trade tariffs on EU steel, abandon the Iran nuclear deal, move the US embassy to Jerusalem, order a Muslim travel ban and retweet anti-Muslim messages from a British far right group.

In turn, the US president has described Britain as being in political "turmoil", criticised its defence spending and shown no enthusiasm for coming to visit: in the 18 months of his presidency, Mr Trump has chosen to visit 17 other countries first.

Whatever this relationship is, it can hardly be described as special.

So this trip is about ticking a diplomatic box, getting a visit out of the way before its further delay became politically embarrassing.

And as working visits go, it is on the minimal side: no Downing Street barbecue, no cabinet visit, no speech to both Houses of Parliament.

The diplomatic aim will be to get through the visit without any gaffes, without upsetting the president, and without him saying anything disobliging about Brexit or a future trade deal.

The UK and the US do have a good relationship at an institutional level, in the fields of defence, security and intelligence. The tricky bit is always the politics and the personalities.

On Friday, Mrs May and Mr Trump will go to watch a joint counter-terrorism exercise by British and US special forces at a military base.

The pair will then travel to Chequers - the PM's country residence in Buckinghamshire - for talks with the foreign secretary.

The president and first lady will travel to Windsor on Friday afternoon to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump's Turnberry golf resort. This part of the visit is being considered private.

The Police Federation has warned the visit will put "unquestionable pressure" on UK police forces as tens of thousands of people are expected to protest against the president in London on Thursday and Friday - and in Glasgow on Friday.

It has also complained that 300 officers working during the visit will have to sleep on camp beds in a gymnasium that has no hot water and restricted access to hot food.

Smaller demonstrations are also expected to be held across the UK, including Devon, Dundee, Edinburgh, Belfast, Norwich, Manchester, Leeds and Liverpool.

Meanwhile, London Mayor Sadiq Khan has granted permission for a giant inflatable figure depicting Mr Trump as a baby to fly over Westminster for two hours on the second day of the president's visit.

But the balloon will not be allowed to fly over his Turnberry golf course, Police Scotland have said.