Father-to-be the Duke of Sussex smiled broadly and appeared relaxed at an Anzac Day service as he awaits the birth of his first child.

With Harry leaving heavily pregnant wife the Duchess of Sussex behind at home to carry out the official royal engagement, bookmakers are now predicting May, rather than April, will be the royal baby’s birth month.

Kate and Harry
The Duchess of Cambridge and the Duke of Sussex attend the Anzac Day Service in central London (Andrew Matthews/PA)

William Hill spokesman Rupert Adams said: “We were as surprised as everyone else that Harry decided to attend a public event as we assumed the baby was imminent.

“We are now odds on that baby will not arrive until May.”

William Hill has it at 4/5 that the baby will be born in May, while Coral now has May at 1-3, followed by April at 2-1 and June as the outsider at 11-4.

Harry on Anzac Day
Harry is looking forward to the birth of his son or daughter (Andrew Matthews/PA)

The duke was a last-minute addition to the royal line-up in Westminster Abbey, where he joined his sister-in-law the Duchess of Cambridge on Thursday afternoon.

Kate, who looked chic in a teal Catherine Walker coat and Rosie Olivia hat, was pictured laughing as she chatted to Harry, dressed in a suit adorned with medals, as they made their way into the Abbey.

Harry had always planned to attend the service and was said to be pleased to be able to join the congregation, but Buckingham Palace only confirmed a few hours before that he would be going.

The duke’s name was not printed in the order of service in case Meghan went into labour with baby Sussex and he was unable to be there.

The official account @SussexRoyal posted about the service on Instagram, including images from 2018 of Harry and Meghan attending a dawn service in London and the Westminster Abbey event together, as well as pictures of the Duke of Cambridge in Auckland and the Duke and Duchess of Sussex in Sydney.

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Today, The Duke of Sussex attends the #ANZACday service at Westminster Abbey with The Duchess of Cambridge and The Duke of Gloucester. The Duke and Duchess of Sussex attended this service last year in addition to the dawn service. They also paid their respects at the #ANZAC memorial in Sydney during their official tour last fall. Having devoted ten years of service to military duty, including two tours in Afghanistan, The Duke completed his time of service with four weeks with the Australian Defence Force. Their Royal Highnesses remain committed to supporting serving members of the Armed Forces, veterans and the families that support them. #ANZACDay commemorates the anniversary of the Anzac landings at Gallipoli in 1916. ANZAC Day is a moment to recognise the Australian and New Zealand Army Corps who lost their lives during the landings, and to honour the sacrifices of men and women in all wars. ANZAC Day has been observed annually in London since King George V attended a service at Westminster Abbey, and more than 2,000 Australian and New Zealand troops marched through the streets. Members of The Royal Family have continued to honour the servicemen and women globally, and today HRH The Duke of Cambridge also paid his respects at @AucklandMuseum. The Duke of Cambridge is visiting The Commonwealth country on behalf of The Queen to pay tribute to those killed in the Christchurch attacks earlier this year.

A post shared by The Duke and Duchess of Sussex (@sussexroyal) on

The post made no mention of the baby but did contain an Americanism, as have previous posts, referring to the couple’s visit to Australia taking place “last fall” rather than in the autumn.

The Duke and Duchess’s new head of communications is Sara Latham, an American with dual US-UK citizenship, who previously worked for Hillary Clinton.

Harry’s presence suggests Meghan is showing no signs so far of giving birth soon, with the duke able to be parted from her to attend the hour-long memorial in central London.

Meghan and Harry
Heavily-pregnant Meghan, with Harry, on one of her final engagements before going on maternity leave in March (Chris Jackson/PA)

American former actress Meghan is likely to be at home in the couple’s newly refurbished Frogmore Cottage in the sanctuary of the Windsor Estate.

The duchess’s mother Doria Ragland is said to have flown from Los Angeles to stay with the couple as they await the birth of the baby, which will be Doria’s first grandchild and an eighth great-grandchild for the Queen.

Doria, Meghan and Harry
The Duchess of Sussex, accompanied by the Duke of Sussex and her mother Doria Ragland at Kensington Palace, London (Ben Stansall/PA)

The name Grace is one of the new favourite names at the bookmakers for a girl, in joint first place with Diana at 6-1 at Coral, with Arthur 8-1 favourite for a boy.

Punters are still predicting a girl, while Coral has also seen a flurry of bets on Meghan giving birth to twins, with odds of 4-1.

Coral’s John Hill said: “The royal baby now looks more likely to arrive in May according to the betting and that is what punters have been rushing in to back over the last 24 hours.

“Grace continues to be the most popular selection in our name betting and it is the girls’ names which are seeing the most money.”

Harry and Meghan
Harry and Meghan (Dominic Lipinski/PA)

The arrival of Baby Sussex will mean Meghan will still be tending to her newborn when US president Donald Trump makes his state visit to the UK on June 3.

Harry could, however, be called upon to meet Mr Trump when the controversial American businessman is entertained by the Queen at Buckingham Palace.

William Hill has odds of 3-1 that seventh in line to the throne Baby Sussex will be introduced to Mr Trump during his stay.