The Duke and Duchess of Cambridge are expecting a baby, St James' Palace announces, as Catherine is taken to hospital suffering from acute morning sickness.

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A spokesman said the Queen and the Duke of Edinburgh, the Prince of Wales and members of Catherine's family were delighted at the news. The pregnancy is said to be in its early stages.

According to the palace, the duchess was admitted to the private King Edward VII hospital this afternoon with a severe form of morning sickness known as hyperemsis gravidarum.

Sources said she was taken to the hospital by car, rather than ambulance. St James's Palace has confirmed that Prince William is at her side. It is thought she had spent the weekend with her parents at their home in Bucklebury in Berkshire.

The Prime Minister, David Cameron, welcomed the news on Twitter, saying he was delighted. "They will make wonderful parents", he said.

Speaking later in Downing Street, Mr Cameron said people around the country would be celebrating. He said he had been told of the news before the official announcement: "I found it quite difficult to keep it to myself", he said.

The leader of the opposition, Ed Miliband, also took to Twitter to pass on his best wishes. "Fantastic news for Kate, William and the country. A royal baby is something the whole nation will celebrate," he wrote.

A spokeswoman at Kate's prep school in Berkshire, where she was seen last week displaying her skills on the hockey pitch, said everyone there was delighted and "absolutely thrilled." And the University of St Andrews, where the couple met, also offered their congratulations.

The royal historian Kate Williams told Channel 4 News the announcement about Kate's pregnancy had taken everyone by surprise. But, she said, the royal family had also been taken by surprise by the new found popularity they have enjoyed since the royal wedding and the Queen's diamond jubilee.

The disasters of the 1990s were a long time ago, she said. "This child will be the most sought after, the biggest source of obsession for a long time to come."

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Rumours have been swirling for the last four days, after Prince William accepted a babygro offered by a well-wisher during a walkabout in Cambridge, telling the woman: "I'll keep that."

I'll keep that. Prince William last week, when he accepted a babygro from a well-wisher in Cambridge

The romper suit featured a picture of a helicopter and the words "Daddy's little co-pilot".

Before her wedding, Kate revealed that she was hoping for children.

"I hope we will be able to have a happy family ourselves," she said.

The child will be third in line to the throne, after the Prince of Wales and Prince William, and legal changes are going through which would give female royals the same rights of succession as boys.

Prime Minister David Cameron explained the constitutional change last year, after 15 Commonwealth countries gave their agreement: "Put simply, if the Duke and Duchess of Cambridge were to have a little girl, that girl would one day be our queen."

Last month, Nick Clegg said that the change in the rules of succession would be effective from last October, when the Commonwealth heads of government met in Perth, Australia. That means it would apply to the duke and duchess's child.

For the moment, the duchess will be staying in hospital for several days. The rare form of morning sickness which she is suffering from causes severe vomiting, leading to dehydration and weight loss - and must be treated with extra nutrients and hydration.

Consultant obstretrician Daghni Rajasingham, from the Royal College of Obstetricians and Gynaecologists, said the length of a woman's hospital stay would depend on how well she was able to keep down fluids.

The condition is most common during the first twelve weeks, although St James's Palace has not confirmed how far along Kate is in her pregnancy.