Kate, Duchess of Cambridge: First picture since pregnancy announced

Duchess of Cambridge, Kate Middleton, appears at first official engagement since it was announced she is expecting second child with Prince William

The Duchess of Cambridge leaves the Royal Garden Hotel

The Duchess of Cambridge said she was glad to "get out of the house" as she carried out her first official engagement since announcing that she is expecting her second child.

The Duchess, commonly known as Kate Middleton, greeted Tony Tan Keng Yam, the president of Singapore, as he began a state visit to Britain.

She wore a grey Alexander McQueen coat and matching coloured hat by Jane Taylor for the occasion, although there was little sign of her baby bump.

The Duchess, who is just over 12 weeks pregnant with her second child, is suffering from a rare form of morning sickness which has forced her to miss a string of engagements since the summer.

However, her condition had improved sufficiently to allow her to play a role in President Tan's state visit on Tuesday.

She made the short trip with her husband, the Duke of Cambridge, from their Kensington Palace apartment to the five-star Royal Garden Hotel in central London to greet President Tan and his wife Mary.

Having arrived at the hotel the couple took a lift to the president's suite, where they met the Singaporean leader and his wife for the first time since September 2012 when the royal couple traveled to Singapore as part of their Diamond Jubilee tour.

The Duchess drew a laugh from the president when she told him, "It's a bit colder than our last meeting". He replied: "The weather is lovely."

Mrs Tan said she was glad Kate could make the engagement and the Duchess replied: "So am I. I've been looking forward to getting out of the house, that's for sure."

The Cambridges posed for an official picture with the president and Mrs Tan before sitting down to tea.

The president commented on the view of Kensington Palace from the hotel, prompting the Duke to joke: "You can probably see into our bedroom window which is a bit worrying - I wouldn't look too closely."

Following their meeting at the hotel, the group travelled by car to Horse Guards Parade, where the Singaporean leader was formally greeted by The Queen and Duke of Edinburgh.

The Duchess of Cambridge leaves the Royal Garden Hotel

The Duchess of Cambridge leaves the Royal Garden Hotel (Julian Simmonds)

Also present at the ceremony were David Cameron, Theresa May, the Home Secretary, and Philip Hammond, the Foreign Secretary, as well as a series of military chiefs and Sir Bernard Hogan-Howe, the Met Police commissioner.

The event was the first time the Duchess has been seen at an official engagement since her second pregnancy was announced on September 8.

Kensington Palace has said she has been suffering from from the rare form of morning sickness hyperemesis gravidarum, which she also experienced while she was pregnant with Prince George.

The Duchess's last official event was in early August when she visited the Tower of London with the Duke and Prince Harry to see the First World War ceramic poppy installation.

Her appearance on Tuesday came after Kensington Palace announced on Monday that her second baby is due in April.

Following the formal ceremony the Cambridges joined the Queen, wearing a navy Karl Ludwig coat and dress, and the Duke of Edinburgh in a carriage procession to Buckingham Palace along with President and Mrs Tan.

The Duke and Duchess travelled in the Scottish state coach, built in 1830 accompanied by Grace Fu, Singapore's second minister for foreign affairs.

The Duke, smartly dressed in a dark suit, shirt and tie, was due to stay at the palace to join a private lunch which The Queen was hosting for the president, leaving the Duchess able to return to Kensington Palace to rest.

Later on Tuesday, the Duchess attended the Wildlife Photographer of the Year 2014 awards ceremony in her role as patron of the Natural History Museum.

Sir David Attenborough introduces the Duchess of Cambridge to digintaries at the event

Sir David Attenborough introduces the Duchess of Cambridge to dignitaries at the museum (Arthur Edwards)

At Horse Guards Parade, President Tan inspected a guard of honour of 96 servicemen and officers from the 1st Battalion Grenadier Guards, as a royal salute of 41 guns was fired in nearby Green Park by The King's Troop Royal Horse Artillery.

He is the first Singaporean head of state to make a state trip to Britain and he will spend his four-day trip conducting a busy round of meetings, visits and bilateral talks, including with the Prime Minister.

Later on Tuesday, after a private lunch at Buckingham Palace, the Queen took the president and his wife on a tour of an exhibition of Singapore-related items, from the Royal Collection, in the picture gallery.

The Duchess of Cambridge at the National History Museum

The Duchess wearing a blue Jenny Packham gown (Eddie Mulholland)

In the evening, the Queen hosted a state banquet at the palace for her guest and both heads of state will make speeches.

On Wednesday, the president will hold talks with David Cameron and will also be guest of honour at a banquet at the Guildhall given by the Lord Mayor.

Kate's last official event was in early August when she visited the Tower of London with William and Prince Harry to see the First World War ceramic poppy installation.

The latest announcement about her pregnancy was made after the Duchess passed the 12-week mark, suggesting a due date in late April.

It could coincide with the Queen’s birthday, on April 21, or the Duke and Duchess’s wedding anniversary on April 29.

Any later and the baby will arrive as the country prepares to vote in next year’s general election on May 7. The baby will become the fourth in line to the throne, behind Prince George.