The Duke and Duchess of Cambridge are expecting their third child, Kensington Palace has announced.

In a statement the palace said the duchess was suffering from severe morning sickness, as she did with her previous pregnancies, so a public engagement she had later on Monday had been cancelled.

The statement said: "Their royal highnesses the Duke and Duchess of Cambridge are very pleased to announce that the Duchess of Cambridge is expecting their third child.

"The Queen and members of both families are delighted with the news.

"As with her previous two pregnancies, the Duchess is suffering from Hyperemesis Gravidarum.

"Her royal highness will no longer carry out her planned engagement at the Hornsey Road Children's Centre in London today.

"The Duchess is being cared for at Kensington Palace."

It was always thought that the Duke and Duchess of Cambridge would go on to have three children.

Kate is one of three and had a happy home life with her sister, Pippa Matthews, and brother, James Middleton, and is close to both of her siblings.

By having more than two offspring, William and Kate are following in the footsteps of the Queen and the Duke of Edinburgh, who went on to have four children - although there was a gap of 10 years between their second child, Anne, and third, Andrew.

An age gap of less than two years between Prince George and Princess Charlotte gave Kate enough time to try for a third before she reached her late 30s, when women's fertility starts to decline more rapidly.

But William - who is one of two siblings - may have needed more convincing.

On an overseas tour to Singapore in 2012, when he was asked by a group of teenagers how many children he would like to have, he said he was ''thinking about having two''.

The couple talked openly of having a family when they announced their engagement and planned ahead by saving the top of their wedding cake - traditionally served at the christening of a first-born.

It is unlikely they will follow in the footsteps of William's great-great-great-great-grandmother Queen Victoria, who had nine children. Despite her large brood, domineering Victoria disliked being pregnant and was said to not be at all maternal.

Betting on a third child for William and Kate began to take off in the run-up to Charlotte's christening when the princess was only nine weeks old.

On a royal tour of Poland in July 2017, Kate joked about having a third - after being given a present designed for newborns.

She speculated about the prospect of another child when she was offered a cuddly toy designed to soothe tiny babies during an event for start-up tech companies in Warsaw.

Saying thank you for the present, she turned to the Duke, laughing, and said: "We will just have to have more babies.''