Britain's Prince William and his wife Catherine, the duchess of Cambridge, are expecting a baby.

A spokesman said the duchess has been admitted to a London hospital on Monday with acute morning sickness and is likely to stay for several days.

"Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting a baby," the prince's office said in a statement.

"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall and Prince Harry and members of both families are delighted with the news."

The couple, officially known as the Duke and Duchess of Cambridge, married in April last year.

There was no detail about when the baby was due, although the prince's spokesman said she was less than 12 weeks pregnant.

"I'm delighted by the news that the Duke and Duchess of Cambridge are expecting a baby," Prime Minister David Cameron said on his Twitter website.

William, Queen Elizabeth's grandson, is second in line to the British throne, and their first child will become the third in succession when he or she is born.

The child will one day be head of the armed forces, supreme governor of the Church of England and subsequently head of state of 16 Commonwealth countries.

Last year Britain and other Commonwealth countries, which have the queen as their monarch, agreed to change the rules of royal succession so that sons would no longer have precedence as heir, regardless of age.

The agreement also means an end to a ban on a future monarch marrying a Catholic, a stipulation dating back some 300 years.

William and Catherine currently live in north Wales where the prince is based as a Royal Air Force search and rescue pilot.