The Prince of Wales arrived in York for a visit to local landmarks, and he will later be joined by his wife Camilla, the Duchess of Cornwall.
His son William is by Kate's side in the Lindo Wing of St Mary's Hospital in Paddington, central London, where the couple drove when she went into labour shortly before 6am.
The Queen today returned to London after spending the night at Windsor Castle, travelling by car to Buckingham Palace.
Return: The Queen arrived at Buckingham Palace this afternoon after leaving Windsor Castle
New child: But it is not yet known when the Queen will meet her new grandchild for the first time
Return: The Queen is set to be in London when the Duchess of Cambridge gives birth
Great-grandmother: The Queen left Windsor Castle this afternoon on her way back to Buckingham Palace
Visit: While his daughter-in-law went into labour, Prince Charles tried out a steam train at the National Railway Museum in York
But Charles is more than 200 miles away in the North of England, showing that not even the most exciting family drama can stop him carrying out his Royal duties.
He arrived at the National Railway Museum in York by steam train as he began a two-day visit to Yorkshire today.
The Prince stepped off the Royal Carriage through clouds of steam, to applause and cheers from the crowd.
The carriage was pulled into the museum by Bittern, the sister engine of Mallard, which marked 75 years as the world's fastest steam train earlier this month.
Dedicated: The Prince was not distracted from his Royal duties by the news the Duchess of Cambridge had gone into labour
As he alighted, he spoke to well-wishers who had turned out to welcome him.
Alex Dickinson and her sons, Thomas, seven, and Freddie, five, travelled from nearby Church Fenton to catch a glimpse of Charles.
She wished the Prince well with the birth of his grandchild as her children gave him a picture of a giraffe for the baby.
She said her son Freddie had said the royal baby was coming in six hours, to which Charles replied: 'Yes, it may well be.'
Asked by another bystander whether there was any news from the hospital, the Prince replied: 'Absolutely nothing at the moment - we're waiting.'
Gift: The Prince was handed a teddy by members of the crowd outside the museum
Record: The Prince is the patron of celebrations
to mark the 75th anniversary of the day the Mallard broke the world
speed record when it reached 126mph on the East Coast Main Line in July
1938
Tour: The Prince of Wales was shown the Doncaster-built Mallard and the museum's collection of royal carriages
On his visit Charles blew the whistle of the Doncaster-built Mallard, which broke the world record for steam when it reached 126mph on the East Coast Main Line in July 1938. It is now a permanent exhibit at the museum.
He met retired Mallard driver Bernard Bell, 89, who once transported the Queen on a royal visit when he was working as a fireman on another locomotive.
Mr Bell, from York, who drove Mallard, Bittern and similar engines for decades, said: 'He was very interested in the locomotives and he asked me all sorts of questions about my driving. It's the first time I've met him and he seemed very nice.'
Charles also looked round the museum's collection of royal carriages, including Queen Victoria's favourite carriage, King Edward's saloon and Queen Elizabeth's saloon, used by the Royal Family during the Second World War.
The visit was the first event of the tour of Yorkshire by the Prince, who will be joined by the Duchess of Cornwall tomorrow when he will visit rural communities before ending up in the seaside town of Bridlington.
He then moved on to York Minster, where he was greeted by cheering crowds and the Archbishop of York, John Sentamu.
Smiling: The Prince seemed happy and relaxed will looking around the museum's collection of trains
He walked through the magnificent interior of the Gothic cathedral with the Archbishop as tourists stopped to take photographs.
He was given a private tour of a recently opened state-of-the-art visitor attraction, Revealing York Minster, in the Undercroft before moving on to the workshops to talk to the craftsmen and apprentices restoring the building.
Charles even had a go with a chisel and a hammer as he talked to the stonemasons.
The Dean of York, the Very Reverend Vivienne Faull, said: 'We're proud and excited that he's come today - but especially today because, in the life of his family, this is going to be such an important day.'
The Dean said she was especially pleased the Prince took such an interest in the apprentices working at the Minster.
As the Prince left the workshops, in glorious sunshine, he was greeted by crowds shouting 'congratulations'.
One York resident, John Dowson, had a joke with the Prince, shouting out 'It's triplets!' as a joke and receiving a generous laugh in return.
On duty: Prince Charles, pictured in York today,
and the Queen, pictured last week, are carrying out their schedules as
normal despite the Duchess of Cambridge going into labour today
Couple: William and Kate drove to the hospital around 6am today to prepare for the birth of their child
Hospital: Kate is in labour in the Lindo Wing of St Mary's Hospital in Paddington, central London
Charles has rarely commented publicly on the impending birth, but earlier this month he asked a women's group if they had any tips on being a good grandparent during to a trip to Kenfig in Wales.
One 74-year-old grandmother told him, 'Spoil them - enjoy it,' leading him to reminisce about happy memories of his own grandmother, the Queen Mother.
The Queen was kept informed about Kate's condition when she was at Windsor castle, and travelled to Buckingham Palace early in the afternoon.
Prince Harry is at RAF Wattisham in Suffolk, where he is based with his squadron of Apache helicopter pilots, and is said to be very excited about becoming an uncle for the first time.
The Earl of Wessex is currently in Devon.
The whereabouts of the other Royals is not known, but it is believed that William is the only relative to have joined Kate in hospital today.
Last week, the Queen suggested that she was keen to see the baby - her third great-grandchild - as soon as possible.
During a trip to the Lake District, 10-year-old Fay Batey asked Her Majesty whether she wanted the child to be a boy or a girl.
The Queen replied that she did not mind, but added: I would very much like it to arrive because I’m going on holiday soon... I wish it would hurry up.'
Her Majesty is apparently set to travel to her private Balmoral estate in Scotland for her summer holiday in the next few days.
The Duke of Cambridge, who has temporarily been off duty from his role as an RAF rescue pilot, will take two weeks of paternity leave after the birth.