Video report by ITV News Correspondent Dan Rivers
US President Donald Trump has said the first part of his three-day state visit is "going really well".
After an afternoon where he was welcomed to the UK by the Queen, Mr Trump said on Twitter that the "entire Royal Family have been fantastic".
The president and First Lady Melania Trump had earlier arrived by helicopter at Buckingham Palace and were greeted by Prince Charles and Camilla, as they stepped off Marine One.
The pair were then taken to meet the Queen - their second introduction following Mr Trump's working visit to Britain last summer.
The monarch warmly greeted the couple, smiled broadly and shook Mr Trump's hand, before they headed inside Buckingham Palace with the First Lady and the Duke and Duchess of Cornwall.
Mr Trump's state visit was marked by the booming sounds of a double gun salute in nearby Green Park, which echoed around the palace grounds.
Soldiers from the King's Troop Royal Horse Artillery took part in the 41-gun salute to honour the president's state visit.
The president was invited to inspect the Guard of Honour, along with Prince Charles, who formed two lines and were wearing their famous scarlet tunics and bearskins.
Watching from a palace balcony overlooking the garden was Mr Trump's daughter Ivanka and her husband - the president's adviser Jared Kushner.
After a private lunch, the extended Trump family were shown items of historical significance to the US from the Royal Collection, on display at Buckingham Palace.
Mr and Mrs Trump were given a special tour by the Queen, while the Duke of York showed Ivanka and her husband Mr Kushner around the exhibition.
The president and First Lady then visited Westminster Abbey, where they were greeted by the Duke of York and helped to lay a wreath at the tomb of the unknown solider.
A wreath was laid in honour of the two World Wars and more recent conflicts, as is tradition with a state visit - President George W Bush laid a wreath in 2003 and President Obama in 2011.
Standing at the grave, the president touched his hand on the wreath and kept his eyes closed during the prayer.
Prince Charles and Camilla welcomed the president at their home, Clarence House, for tea where they posed for pictures, before moving to private quarters for tea.
A large crowd gathered outside Buckingham Palace in the sunshine as they awaited the arrival of the Trumps.
A huge security operation is in place for the visit, and police officers could be seen standing at three different points on the roof at the front of the palace.
Scores of uniformed police officers are in position across London, with The Mall and other roads in front of the palace closed to traffic and completely deserted.
The couple touched down at Stansted Airport on Monday morning and were met by Foreign Secretary Jeremy Hunt and US Ambassador to the UK, Woody Johnson.
The president will attend a state banquet hosted by the Queen later on Monday and will meet Theresa May, in her final days as Prime Minister.
As his plane landed in the UK, Mr Trump launched a Twitter tirade at London Mayor Sadiq Khan, branding him a "stone cold loser" and wrote he had "done a terrible job" as mayor.
Mr Trump's tweet added: "[Mr Khan] has done a terrible job as Mayor of London, has been foolishly “nasty” to the visiting President of the United States, by far the most important ally of the United Kingdom. He is a stone cold loser who should focus on crime in London, not me......"
In return the Mayor's office fired back, saying Mr Trump was offering "childish insults which should be beneath the President of the United States".
Mr Khan said the UK should not "roll out the red carpet" for Mr Trump and offer him the red carpet.
Mr Trump and the First Lady were greeted with a guard of honour by airmen from the RAF Regiment as they walked off Air Force One.
They will be staying at Winfield House, the home of the US Ambassador during their three-day visit.
The couple are not staying at Buckingham Palace, due to restoration works which are on going.
What is Donald Trump doing during his visit to the UK?
In the evening, Mr Trump will attend a state banquet hosted by the Queen at Buckingham Palace.
The Duke and Duchess of Cambridge will be in attendance, as will Prime Minister Theresa May, US business people and other dignitaries.
On Tuesday, Mr Trump and Mrs May will co-host a business breakfast meeting with senior UK and US business leaders. The event at St James’s Palace will also be attended by the Duke of York.
In the evening, the US President will host a dinner at the US Ambassador's residence, Winfield House.
On Wednesday, Mr and Mrs Trump will join the Queen and Prince Charles at Southsea Common in Portsmouth to commemorate the 75th anniversary of D-Day.
Later on Wednesday, after the UK state visit has come to an end, Mr and Mrs Trump will travel to the Republic of Ireland to stay overnight at his Doonbeg hotel and golf resort in Co Clare.
During his visit he will hold a bilateral meeting with Irish premier Leo Varadkar at Shannon Airport.
What are the protests planned?
Protests are planned in cities across the UK on Tuesday, and the giant inflatable Donald Trump, made famous during Mr Trump's visit to the UK in July 2018, is expected to fly over London again.
Organisers plan to fly the 20ft blimp above Parliament Square for two hours from 9am on Tuesday, the second day of Mr Trump’s UK visit, after its owners reached their fundraising target.
Protesters gathered outside Buckingham Palace on Monday, and police officers were forced to intervene to break up a heated exchange.
Although Mr Trump visited the UK in July 2018 and met both the Prime Minister and the Queen, that was not a state visit, but a working one.
Protesters opposed to the president's visit to Ireland launched a series of demonstrations across Ireland on Monday.
The president is travelling to Ireland on Wednesday, after his three-day visit to the UK.