The Duchess of Cambridge is being treated for severe morning sickness after being whisked to an exclusive Marylebone private hospital yesterday from her parents’ Berkshire home.

Kate Middleton is expected to stay at King Edward VII’s Hospital Sister Agnes in Beaumont Street for the next few days. The Duke of Cambridge was at her bedside yesterday and is expected to return to the hospital today. Visits from the Duchess’ immediate family - her parents Carole and Michael Middleton and sister Pippa - are also likely.

William spent yesterday with Kate after the royal couple announced the Duchess was expecting her first child but had developed a rare condition which can leave expectant mothers dehydrated and under weight.

Known as hyperemesis gravidarum it can leave women unable to keep down food and fluids, and carrying twins may increase the chances of developing the illness.

But while there is concern for the royal couple, there is excitement across the UK and beyond of news of a baby who will become third in line to the throne, with messages of support sent from leading figures both at home and abroad.

Prime Minister David Cameron, who was informed by note in the middle of a meeting, led the congratulations from the nation when he said: “It’s absolutely wonderful news and I’m delighted for them. I’m sure they will make absolutely brilliant parents, and I’m sure everyone around the country will be celebrating with them tonight.”

The Queen and Duke of Edinburgh, the Prince of Wales and members of both families are delighted with the news, said a St James’s Palace spokesman.

A statement released yesterday read: “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 were reportedly hoping to keep news of Kate’s pregnancy quiet until after Christmas, as she has not passed the 12-week point, but yesterday’s announcement was prompted by the Duchess’s medical condition.

The St James’s Palace statement added: “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.”

A spokesman would not say when the royal couple became aware of the pregnancy, only saying “recently”.

Speculation is also growing as to whether the Duchess will elect to have her baby in the private Lindo Wing of St Mary’s Hospital in Praed Street, Paddington, the neonatal unit of choice for the royals for the last two generations.

Prince William and his brother Harry were born there, as were Zara and Peter Philips, the Princess Royal’s children.

Meanwhile, congratulations for the Duke and Duchess poured in from around the world. Jay Carney, press secretary to US president Barack Obama, said: “On behalf of everyone here in the White House, beginning with the President and the First Lady, we extend our congratulations to the Duke and Duchess of Cambridge on the welcome news this morning out of London that they are expecting their first child.”

Asked if Mr Obama had any advice as parents, he said: “I haven’t had that conversation with them, but I know they both feel that having a child is one of the most wonderful parts of their lives.

“So I’m sure that will be the same for the Duke and Duchess of Cambridge.”

Kate’s illness can also lead to the build-up of toxins in the blood and urine.

The Duchess is likely to be taking anti-sickness tablets and have a drip in her arm so she can receive fluids intravenously.

But her symptoms of severe vomiting may last for much of her pregnancy.

Yet, at her last public engagement on Friday, at her old prep school St Andrew’s in Pangbourne, Berkshire, the Duchess appeared well, had lunch with pupils and staff and played hockey in three-inch-high calf-length boots.

A spokeswoman for St Andrew’s said they had “no inkling at all” that she was expecting.

News that Kate’s condition may indicate she is carrying twins prompted bookmaker William Hill to cut the odds of the royal couple having two babies from 33/1 to 25/1 following a number of bets overnight.

Victoria and George were the best backed names during the first 12 hours following the announcement, offered at 10/1.