Duke and Duchess of Cambridge expecting a baby

But St James’s Palace said in a statement that Kate had been admitted to a private hospital for treatment for a severe form of morning sickness known as hyperemesis gravidarum.

St James’s Palace said in the statement: “The Duchess was admitted this afternoon to King Edward VII Hospital in central London with hyperemesis gravidarum.

“As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter.”

St James’s Palace would not say when the royal couple became aware of the pregnancy only saying “recently”.

It is understood that the pregnancy has not passed the 12 week point and today’s announcement was prompted by the Duchess’s medical condition.

For women with hyperemesis gravidarum their vomiting can be so severe they cannot keep food or liquid down.

The condition usually continues past the first three months of pregnancy and can pass by week 21, but may also last longer.

Reacting on Twitter, Prime Minister David Cameron wrote: “I’m delighted by the news that the Duke and Duchess of Cambridge are expecting a baby. They will make wonderful parents.”

A spokeswoman at Kate’s old prep school, St Andrew’s in Pangbourne, Berkshire - where she showed off her hockey skills last week in an Alexander McQueen frockcoat and three-inch-high calf-length boots - said they had “no inkling at all” that she was expecting.

She said: “Obviously everyone at St Andrew’s are delighted for them both. We’re absolutely thrilled.”

Kate visit to her old prep school on Friday afternoon was her last public engagement.

She appeared well and even had lunch at the school with pupils and staff during the two-hour visit.

So her condition may have developed over the weekend and it is likely she was taken to hospital this afternoon after seeking medical advice.

Hyperemesis gravidarum can be serious but Kate was driven to the King Edward VII Hospital in a car and not an ambulance.

The Duchess had a number of engagements this week, including a visit to London’s Docklands on Wednesday for a charity fundraising session on a brokers’ trading floor, but they have all been cancelled, said St James’s Palace.

Labour leader Ed Miliband responded on Twitter: “Fantastic news for Kate, William and the country. A royal baby is something the whole nation will celebrate.”

A spokesman for the Royal Air Force (RAF), with which William serves as a search-and-rescue pilot, said: “The RAF is delighted with the news and wishes the Duke and Duchess of Cambridge all the best for the future.”

Scottish First Minister Alex Salmond offered his congratulations to the couple, who are known as the Earl and Countess of Strathearn when in Scotland.

Mr Salmond said: “My warmest congratulations and sincere best wishes to the Earl and Countess of Strathearn on this wonderful news. Everyone in Scotland will join me in wishing the couple the very best as they prepare for the birth of their first child.”

A spokeswoman for the University of St Andrews, where Kate and William met, said: “We are delighted for the couple and will be writing to them to offer our congratulations. They must be very pleased.”

St James’s Palace confirmed that William is by his wife’s side in hospital but would not comment on whether he travelled with her to hospital.

Kate made the journey from Bucklebury in Berkshire, where her parents Michael and Carole Middleton live, and it is thought she spent the weekend with them.

William’s uncle Earl Spencer welcomed the announcement, saying in a statement: “It is wonderful news and I am thrilled for them both.”

The baby would have been a first grandchild for William’s late mother and the Earl’s sister, Diana, Princess of Wales.

The Archbishop of Canterbury, who married the royal couple in Westminster Abbey in April 2011, said: “The whole nation will want to join in celebrating this wonderful news.

“We wish the Duchess the best of health and happiness in the months ahead.”