Appleton, 33, had often spoken in the past about wanting to marry her rock star boyfriend, who fronts the group, once notorious for their bad behaviour.
The couple have been together for nearly eight years and she is credited with taming the singer's notoriously hard drinking and abrasive attitude. The Oasis singer married actress Patsy Kensit in 1997 but split three years later.
The small wedding party then reportedly moved to the nearby five-star Landmark Hotel.
Guests included Appleton's former pop star sister Natalie, and her husband Liam Howlett, of The Prodigy.
Liam's fascination with music began during primary school, when he fell for Ska and Two Tone.
On moving up to secondary school, he was immediately attracted to the hip-hop culture, became fascinated by bands like Grandmaster Flash & the Furiuos Five.
Gallagher had Lennon, eight, with Kensit, and nine-year-old daughter Molly with singer Lisa Moorish.
The perennial Met Bar partying during their time in the pop band All Saints, which opened deep fissures between the pair and their erstwhile best friends and fellow band members, Melanie Blatt and songwriter Shaznay Lewis.The singer married at a low-key ceremony at London's Westminster Register Office.Liam's brother and bandmate Noel, did not attend the ceremony because he was in Los Angeles, according to reports.What is it about the Appleton sisters that gets people's backs up?Why have they come to occupy an unenviable space in public consciousness - somewhere between Chardonnay from Footballers' Wives and Mira Milosevic - inspiring equal parts condescension and contempt?