The Duke and Duchess of Cambridge are “very pleased to announce” that they are expecting their second child, Clarence House said.

As with her first pregnancy, Kate is suffering from acute morning sickness and is being treated by doctors at Kensington Palace.

Clarence House confirmed that the Duchess will not be joining her husband on a planned engagement in Oxford today.

Prime Minister David Cameron said: “Many congratulations to the Duke and Duchess of Cambridge. I’m delighted by the happy news that they’re expecting another baby.”

The couple recently spent a fortnight in their Norfolk retreat Amner Hall, in the Sandringham Estate, which is hotly tipped to become the family’s future home.

Midway between Norwich and Cambridge, the Georgian house is the ideal location for Prince William’s new role as a pilot for the East Anglian Air Ambulance.

It was confirmed at the start of August that the Prince would take up the full-time role, which he has begun training for this month.

The Duke will start as a co-pilot but, after a period of training, will be qualified to fly as a helicopter commander.