Duchess Catherine and Prince Louis. Picture: Matt Porteous

London - He famously slept through most of his big day last week. But here is proof that three-month-old Prince Louis already has the mischievous Cambridge twinkle in his eye.

The little prince is seen smiling for the first time in this charming picture with his mother, taken after his christening eight days ago.

And it shows how Louis is almost the spitting image of Kate when she was a baby. The photograph was captured by Matt Porteous, who had been employed by the Duke and Duchess of Cambridge to take some intimate snapshots for their private family album following the christening in the Chapel Royal at St James’s Palace.

It has been released in addition to the four formal portraits, taken by Matt Holyoak, issued by Kensington Palace. William and Kate so loved this picture by Mr Porteous, who took Prince George’s official third birthday photographs, that they decided to make it public.

It was taken in Prince Charles’s gardens at Clarence House, where the christening party took tea – and a slice of the cake kept for the occasion from William and Kate’s wedding.

Joyously natural, the photograph shows the duchess, 36, elegant in cream Alexander McQueen and an elaborate Jane Taylor headpiece, holding Louis, in the Queen’s Honiton lace christening gown, a replica the monarch had made of the original gown created for Queen Victoria’s children.

"Their Royal Highnesses hope that everyone enjoys this lovely photograph of Prince Louis as much as they do," Kensington Palace said.

While Mr Holyoak’s stunning pictures, published in the Daily Mail, were for the public record, this picture had been intended just for the family and friends, aides added.

As a babyhood picture of Kate taken in 1982 shows, Louis bears a striking resemblance to her.

Now old enough to laugh and show an interest in the world around him, he is some months away from taking his first steps.

But no doubt when he does, he will join his brother Prince George, who turns five on Sunday, and sister Princess Charlotte, three, in giving his parents the runaround.