Boris Johnson led tributes to the Duke of Edinburgh in a statement outside Downing Street.
The Prime Minister said it was to Her Majesty and the Royal family that thoughts must turn.
He said:” We mourn today with her Majesty the Queen, we offer our condolences to her and all her family and we give thanks as a nation and the kingdom for the extraordinary life and work of Prince Philip, Duke of Edinburgh.”
The Prime Minister paid full tribute to the Duke’s public life and service but reserved special praise for support of the Queen.
Johnson said: ” We remember the Duke for all of this and above all for his steadfast support for Her Majesty the Queen. Not just as her consort by her side every day in her reign, but as her husband, her strength and stay of more than 70 years.”
The flags in Downing Street were lowered to half-mast following the death of the Duke of Edinburgh.
Philip, 99, was the longest-serving consort in British history.
Labour leader Keir Starmer tweeted: “The United Kingdom has lost an extraordinary public servant in Prince Philip. Prince Philip dedicated his life to our country – from a distinguished career in the Royal Navy during the Second World War to his decades of service as the Duke of Edinburgh.”
Government ministers and other senior politicians offered tributes to the Duke on social media.
Veterans minister Johnny Mercer tweeted: “Tragic news. A true patriot.”
Vaccines minister Nadhim Zahawi posted: “This is a sad sad day for us all. May he rest in peace. RIP Great Prince.”
Scottish First Minister Nicola Sturgeon earlier tweeted condolences on behalf of the Scottish government.
She said: “I am saddened by news that the Duke of Edinburgh has died. I send my personal and deepest condolences – and those of the Scottish Government and the people of Scotland – to Her Majesty The Queen and her family.”
The Union Jack flag on Buckingham Palace is flying at half mast following the Duke of Edinburgh.
Increased numbers of police officer were patrolling beside the palace gates where small groups of passers-by have also gathered.
Prince Philip died at Windsor Castle weeks after being discharged from a month-long stay in hospital.