Prince Philip in hospital for operation on abdomen
The Duke of Edinburgh is due to have an exploratory operation on his abdomen after spending the night in hospital.
The Queen's husband, who will be 92 on Monday, was admitted to the London Clinic on Thursday and is expected to stay in hospital for about two weeks.
Buckingham Palace said the admission was pre-arranged and not an emergency.
Prime Minister David Cameron said the duke was held in the "highest esteem" by the British people and the whole country would be wishing him well.
The Queen is continuing with her engagements for the day, and has officially opened the BBC's rebuilt Broadcasting House in central London.
As the Queen toured the BBC's new headquarters, Radio 4 Today programme presenter John Humphrys asked her how the Duke of Edinburgh was.
"I don't know," she replied, before adding: "He's not ill."
The duke went to hospital straight after a Buckingham Palace garden party on Thursday afternoon. Guests said he showed no signs of being unwell.
Prince Philip will undergo surgery under general anaesthetic and the Palace said in a statement that further updates would be issued "when appropriate".
The prime minister sent a personal message to the Duke of Edinburgh on Thursday wishing him a speedy recovery.
He said the duke was an "extraordinarily dedicated public servant".
"I know the whole country will be thinking about him, thinking about the family and wishing him well," he added.
Meanwhile, Prince Philip's grandson, Peter Phillips, said he was in "good hands".
Speaking at a show jumping event in east London, he said: "We are being kept up to date in terms of what's happening, but he's one of those people who just wouldn't want you to stop because he's gone into hospital."
In the past week, the duke has been having unannounced "abdominal investigations" at the hospital in central London, where police officers have been standing guard outside.
Prince Philip pulled out of an engagement for the Royal National Institute of Blind People on Monday, after becoming unwell ahead of attending a service at Westminster Abbey marking the 60th anniversary of the Queen's coronation.
The Queen had been due to visit the BBC's £1bn headquarters with the duke, but instead carried out the engagement alone.
The monarch met personalities such as Sir Bruce Forsyth and David Dimbleby, and watched The Voice star Danny O'Donoghue sing with his band The Script in Radio 1's Live Lounge.
The Queen was shown around the state-of the-art broadcasting centre - home to BBC News and World Service among others - by BBC director general Tony Hall and BBC Trust chairman Lord Patten, as well as meeting journalists in the newsroom.
The last time the Queen visited Broadcasting House was seven years ago to mark the 80th anniversary of the corporation's Royal Charter.
In April, Buckingham Palace played down fears about the Duke of Edinburgh's health after he was pictured in Canada with purplish skin around his eye.
It said he did not fall and simply woke up with the discoloration.
Prince Philip has been admitted to hospital three other times in the past two years after suffering health scares.
After attending events to mark the Queen's Diamond Jubilee a year ago, he went to hospital for five nights after sustaining a bladder infection.
He spent four days in hospital over Christmas 2011 following an operation to clear a blocked heart artery.
In August 2012, he was treated at Aberdeen Royal Infirmary for a bladder infection.
Kate Williams, royal historian at Royal Holloway, University of London, said Prince Philip "is a man who is determined to carry on".
She added: "He has had seven public engagements this week. There probably aren't many people across the country in their 90s who are keeping up such a schedule."
Simon Galloway, a consultant general surgeon at the University Hospital of South Manchester, said a fortnight is a "fairly lengthy" hospital admission but it was not usual for someone of the duke's age.