Royal aides said the decision to go public "was very much driven by the duke and duchess", who knew it would be impossible to keep the news a secret in the age of Twitter. "It's a very hard thing to go public at such an early stage, but they wanted to be open with people as much as possible," said one.

The Queen, the Prince of Wales and Prince Harry, who was contacted in Afghanistan, were all told the news on Monday afternoon before St James's Palace made the announcement at 4.01pm. It was the first royal baby to be confirmed by Tweet, and the Twitterverse exploded with congratulations and comment at the royalbaby hash-tag.

Meanwhile Kate remained in hospital attached to a drip to replace the fluids and nutrients she is losing through continual vomiting. Her illness, which affects fewer than four in every 1,000 pregnant women, can lead to dehydration and serious health issues if left untreated.

It often runs until the 14th week of pregnancy and for a few seriously unlucky mothers can last the whole pregnancy, although the doctors filling British television screens with explanations of the problem speculated that this is merely the result of the initial surge of pregnancy hormones for the duchess, suggesting she is six to eight weeks pregnant.

Kate is reportedly being treated by Marcus Setchell, the former gynaecologist to the Queen, who delivered the Countess of Wessex's two children as well as Leo Blair, the son of former prime minister Tony Blair.

The news is a boon for Prime Minister David Cameron, who had been wrestling with Leveson Inquiry fall-out, welfare reform and the Eurozone crisis, but who can now enjoy the wave of public warmth over the news — and the moving of the spotlight away from the serious political agenda.

He was handed a note to tell him the news during a 2pm policy meeting in Downing Street and was among the first to tweet his congratulations: "It's absolutely wonderful news, and I'm delighted for them and I'm sure they will make absolutely brilliant parents."

He said that after he received the note, "I found it quite difficult to keep it to myself."

The child would be third in line to the throne, gazumping its Uncle Harry, and would be destined to be monarch regardless of its sex, as the British Government is negotiating with all Commonwealth countries to change the law so that a first-born girl can be queen even if she has brothers.

If the pregnancy should result in twins — and severe vomiting of Kate's kind has a slight association with multiple pregnancies — the first-born will take the throne.

Prince William was already looking like a new father, emerging from the central London hospital around 8pm on Monday unshaven and unsmiling. He had driven his wife to hospital himself after picking her up from her parents' home in Berkshire.

With Britain still coasting on the high of the Jubilee earlier this year, its media are in a renewed royal frenzy. Serious newspapers began live-blogging on the issue. TV reporters were stationed in the winter cold and dark outside the hospital.

Twitter buzzed with quips like "Dilatey Katie", and when Kate and William put news of her pregnancy up on their website, it promptly crashed.

Meanwhile bookies announced Elizabeth (8/1 ) and Diana (12/1) the top favourite names for a girl and Philip (14/1) and Edward (16/1) for a boy (and you can bet on the hair colour, too, 6/4 brown, 2/1 blond). And columnists began speculating about when, precisely, the baby might have been conceived.

The holiday in France that spawned the topless pictures? Maybe, concluded one paper, though perhaps it could have been during the couple's tour of South-East Asia. Another magazine reports "insider" claims that the baby is the result of a passionate night in their rented home in Wales.

It is a far cry from the way the Queen's pregnancy with Charles was managed. An oblique announcement said merely that she would "undertake no public engagements until June" — and left the world to figure out what that meant.

It wouldn't be Britain with a pinch of bah-humbug. A columnist with the Independent has dubbed the baby "the feel-good foetus". The Telegraph's Tom Chivers tweets that he needs to coin a new word for what he is already feeling:

"Babigue? Pregxhaustion? Ennuioetus?"

Several of the Top Ten Stories Zoe Williams of the Guardian says she doesn't want to read are already up on newspaper websites, including advice on what Kate should and shouldn't be eating and speculation as to how Diana would have reacted. And there are seven more months to go...