Analysis of Google data shows online searches for "How to get wavy hair" exploded 778 percent in the UK on January 9, after pictures of Kate in three different Alexander McQueen gowns, always with the same "timeless" hairstyle, were released in light of her 40th birthday.

       A spokesperson for Longevita, who commissioned the research, said: "The Duchess of Cambridge is undoubtedly one of the most influential women on the planet when it comes to style and these findings only amplify that.

       "The surge in interest for the hairstyles that the Duchess wears can be attributed to her timeless and elegant style.

       "The simplicity of the hairstyle creates a timeless feel to the portraits as well as being a look that is easily emulated by fans."

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       Kate's hairstyle in the shots is not the only element to send royal watchers into a frenzy.

       The red, one-shouldered satin dress she wears in one of the images caused an explosion in searches for "red dress", with analysis showing a 376 percent growth the morning after the release of the birthday portraits, as found by Printique.

       The outfit also features a signature pair of earrings that belong to the Queen, which can be seen as a heartfelt tribute from Kate to the 95-year-old Monarch.

       Another photo, in black and white with Diana's diamond and pearl drop earrings on full display, is thought to been a sweet tribute to the late Princess of Wales.

       Captured at Kew Gardens by Paolo Roversi, the pictures show a side of the mother-of-three which is rarely seen – one that instils "grandeur and modernity" and tells the world she is "finally unafraid to be a fashion template".

       Writing in The Telegraph, author Lisa Armstrong praised the portraits to the point of comparison with those of Her Majesty taken by Cecil Beaton in the 1930s.

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       She said: "The picture of a seated Kate could hang side by side in the National Portrait Gallery with Beaton's 1939 portrait of Queen Elizabeth as a reassuring demonstration of the British monarchy's continuity and its ability to heal itself after family rifts."

       The images of the Duchess will in fact be part of the permanent collection of the National Portrait Gallery, of which she is Patron.

       Interest in Mr Roversi, who described working with Kate as "a true honour" and "a moment of pure joy", spiked massively, too.

       Google searches for him skyrocketed 1,700 percent.

       The photographer, who has worked with top models of the likes of Naomi Campbell and Kate Moss, said: "I was moved by her warmth and friendly welcome and enchanted by her shining eyes that reflected the loveliness of her soul and her smile showing the generosity of her heart."