Prince William has stepped into the row over racism in football, saying there is "sadly more work to do" to eradicate it from the game.
The Duke of Cambridge has vowed to take Prince George to watch his beloved football team, Aston Villa, at Villa Park in the future.
Prince Charles has revealed William and Harry inherited an essential quality from him - his prowess on the dance floor.
David Cameron has hailed the birth of Prince George as a "national moment", but called on the Royal Family to be granted privacy in the future.
Mr Cameron sought to remind the public that the birth was "first and foremost a very private and family event" before a national one, and called on the world's media and the public to give the Duke and Duchess of Cambridge "space and the privacy to get to know their new son."
The Prime Minister said the royal birth was the latest moment that had seen a "surge of affection" for the monarchy:
"The birth of Prince George was a national moment. A time to recognise, once again, what a vital part of our national life the monarchy is.
"In the past few years we have seen a surge of affection for our Royal Family, from the royal wedding to the Diamond Jubilee and the coronation celebrations. And, of course, this summer millions cheered the news of the royal birth."
Buckingham Palace is to host its first official football match as part of the FA's 150th anniversary celebrations after the Queen gave her permission.
The Duke of Cambridge, who is the president of the FA, helped arrange the game between two of England's oldest amateur clubs in the gardens of the famous landmark.
Civil Service FC and Polytechnic FC, both based in west London, will go head to head in the rarefied surroundings of the palace garden on 7 October.
Wembley groundsman Tony Stones will work with the royal gardeners to create a pitch in the 40-acre garden.
William will host the event and also present medals to 150 grassroots volunteers in recognition of their dedication to the sport. The match is being held in tribute to their commitment.
The Duke of Cambridge is making one of his final public engagements on Anglesey as the new father's time on the island comes to an end.
William will be joined by Kate as he starts the gruelling, three-day annual "ultra" marathon run around the coast of the island, known as the Ring O' Fire.
The Duke and Duchess will meet some of the runners and their families and volunteers before the start - but the couple will not be bringing the royal baby.
The annual event is a 135-mile foot race around the rugged coast of Anglesey, staged over three days and including 13,695 feet of ascent.
The last time the Duchess was seen in public was the day after the birth of Prince George.
Award-winning Press Association photographer Lewis Whyld tweeted:
Lets be honest the new Royal baby photos are not very good, you know, photographically. If you're ill see a doctor, not a mate. Expertise.
@adamblenford yes, the light is terrible. The memory is captured but it's just not very beautiful. A shame and a missed opportunity.
Whyld has been behind some of the most viewed images on the ITV News website, including lightning behind the London Eye, Ed Miliband's egging and a 360-degree photo of the royal baby's first public outing.
Getty's royal photographer Chris Jackson told ITV News Michael Middleton's pictures of Prince George were "charming" and a "good all-round effort".
He said: "In the future, I would recommend taking photos in the early morning or late evening when the light is turning to give a softer light to the image but it's a good all-round effort and it's a very charming image."
Eddie Mulholland, vice chairman of the British Press Photographers Association, told The Daily Telegraph that Michael Middleton's pictures of Prince George were "lovely snaps" but "not what you want for such a historic picture."
He said: "They are lovely snaps for a grandfather to have taken, but in terms of the quality, they are not really what you want for such a historic picture.
"I would be pleased with them if they were for me and my family, but they look like they have been taken with a mobile phone or a consumer compact camera. It would have been better to have seen it done properly given that this is the official record of the future king."
He added: "The photograph with the dogs is the worst. One of the dogs in the corner looks like a furry rug, and part of the Duke’s head is wiped out by a patch of light coming through the trees."
The photographer who took Prince William's baby photos has praised the snaps of the Duke and Duchess of Cambridge with their newborn son, Prince George.
Ian Pelham-Turner gushed he "really loved" that he could "see the love in Kate's eyes towards her father".
Michael Middleton follows a long line of photographers to have captured important images of members of the royal family.
Little is known about how much experience the British Airways flight dispatcher-turned-businessman has behind the lens, but as the first official photographs to be taken of the future king, the pictures are sure to have their place in history.
The intimate family portraits were taken in the garden of the Middleton family home in Bucklebury, Berkshire, earlier this month and for Mr Middleton, they are not only of a future monarch but of his first grandchild.
Martin Keene, head of pictures at the Press Association, said the photographs were impressive. "Any photographer would have been pleased to have taken them," he said.
The first official photographs of Prince George have been released. Lying peacefully in the arms of the Duchess of Cambridge, the newborn, who is third in line to the throne, seems to be sleeping in the pictures.
The intimate pictures were taken by Kate's father Michael Middleton in a shady spot of the garden of the family home in Bucklebury, Berkshire, earlier this month.