Boris Johnson will not attend the Duke of Edinburgh's funeral next Saturday in order to allow "as many family members as possible" to go amid coronavirus restrictions, No 10 has said.
Only 30 people - expected to be the duke's children, grandchildren and other close families - can attend the funeral at St George's Chapel, Windsor.
The public has been asked to stay away.
The Prince of Wales paid tribute to his "dear papa" on Saturday, saying he will be missed "enormously".
Speaking from his Highgrove home in Gloucestershire, Prince Charles said his late father was a "very special person who... above all else would have been amazed by the reaction and the touching things that have been said about him".
The prince said he and his family were "deeply grateful" for this, adding: "It will sustain us in this particular loss and at this particularly sad time."
The duke died at Windsor Castle on Friday, aged 99.
A remembrance service will be held for him at Canterbury Cathedral later this morning.
Funeral arrangements for next weekend, which Buckingham Palace said "very much" reflect Prince Philip's wishes, have been adapted in light of the coronavirus pandemic.
The televised service will be a ceremonial event rather than a large state affair usually associated with the death of a monarch.
A No 10 spokesman said: "As a result of the coronavirus regulations, only 30 people can attend the funeral of HRH The Prince Philip, Duke of Edinburgh.
"The prime minister has throughout wanted to act in accordance with what is best for the royal household, and so to allow for as many family members as possible will not be attending the funeral on Saturday."
Among Royal Family members to attend the ceremony will be the Duke of Sussex, who will fly from his Californian home to the UK.
His wife the Duchess of Sussex, who is pregnant with their second child, has been advised by her doctor not to travel, Buckingham Palace said.
On the day of the funeral, a national minute's silence will be held at 15:00 BST.
Prince Philip's coffin will be transported from Windsor Castle to St George's Chapel in a specially-modified Land Rover he helped to design.
Members of the Royal Family, including the Prince of Wales, will walk behind the coffin, and the Queen will travel separately to the chapel.
Guests will socially distance and wear face coverings in line with coronavirus restrictions.
Military guns will fire during the procession, which will take eight minutes, and the curfew bell will toll.
Eight pallbearers will carry the coffin, draped with duke's standard, with a wreath and the duke's naval cap and sword on top, up the west steps into the chapel. It will be greeted by the Dean of Windsor and the Archbishop of Canterbury.
These 10 people are not included in the number of attendees allowed.
A guest list will be released on Thursday.
Prince Charles paid tribute to his father on Saturday, saying the duke had given the "most remarkable, devoted service" to the Queen, the Royal Family, the country, and the Commonwealth over the last 70 years.
Members of the Royal Family visited the Queen at Windsor Castle following the duke's death.
The Countess of Wessex said "the Queen has been amazing" as she left the castle with the Earl of Wessex.
The Duke of York also visited on Saturday, while the Prince of Wales travelled there on Friday afternoon.
In tribute to the duke, saluting batteries each fired 41 rounds on Saturday in cities including London, Edinburgh and Cardiff, and at Hillsborough Castle in County Down. Guns were also fired in Gibraltar.
There will be eight days of national mourning - to end on 17 April - ahead of the funeral.
Prince Philip will not lie in state - where members of the public would have been able to view his coffin.
His coffin will instead lay at rest in the private chapel at Windsor Castle and will be draped with the duke's personal standard with a wreath of flowers on top.
The Royal Family will observe two weeks of mourning, although royal engagements will continue where appropriate.
A spokesman for the Palace said: "Whilst this is a time of sadness and mourning the coming days will be an opportunity to celebrate a remarkable life."
Under earlier arrangements for the days after the duke's death, codenamed Forth Bridge, thousands of people would have been expected to gather in London and Windsor, with some even camping out to get a vantage point to watch the military procession.
On the Royal Family website, members of the public are asked to consider making a donation to a charity instead of leaving floral tributes in memory of the duke. An online book of condolence is also available for the public to post their personal tributes.
All UK government buildings have been told to fly official flags at half-mast in tribute to the duke until 08:00 on the day after the duke's funeral.
The Duke of Cambridge has withdrawn from giving a speech at the Bafta Awards ceremony on Sunday night, Kensington Palace said. His grandfather was Bafta's first president.
Meanwhile, the Football League has announced that matches scheduled to begin at the same time as Prince Philip's funeral will be rearranged "as a mark of respect".