With their close harmonies in the style of The Andrews Sisters, and playful vintage-style covers of top-charting pop songs, the Puppini Sisters have won more than a few celebrity fans over the 11 years since they first formed.

Cyndi Lauper, Michael Bublé and even Prince Charles are among their admirers, and two weeks ago, they added another star to that list.

“We went to San Francisco recently, and Hugh Laurie happened to be in the audience,” says group founder, Marcella Puppini.

“He’s an excellent musician himself so we were scared out of our wits. But he left us a note after saying he absolutely loved it. What a man!”

The swing trio may hark from another era but right from the start, their retro sound was a hit with with modern-day audiences.

Their 2007 cover of The Bangles’ classic Walk Like an Egyptian was featured on hit TV show Grey’s Anatomy, and back in 2011, Bublé asked them to feature on his now-classic cover of Jingle Bells for his number 1 album, Christmas.

The group are now just about to finish the UK run of shows at the Islington Assembly Hall on May 18 to promote their fifth album, The High Life.

Self-described as a “classic Puppini Sisters record,” there’s covers of standards like It Ain’t What You Do, takes on chart-toppers like Chandelier, and a few originals thrown in for good measure, including the title track: Is This The High Life?

The album is the first produced without the backing of their former label, Universal, after they decided to go independent, and was instead partly funded through an online crowdfunding campaign run by PledgeMusic. More than 800 fans donated in excess of £31,000.

“It fuelled us in the way a record company couldn’t,” muses Puppini.

“It humbles you, and rather than infusing you with the slight anxiety you always have when working with a record company, because you want them to be happy, with our fans, we know what makes them happy,” she adds. “There’s a relaxed quality to this album that we haven’t always had in the past.”

Puppini, a former mayoress of Camden, says their fans are extremely loyal, but so too are the non-related sisters. To give something back, eight fans who pledged £300 or more were given the chance to join them in performing on the album’s bonus track, a cover of Ray Charles’ Hit the Road Jack.

They say the reaction was better than ever expected for the first record released on their own label, Millionaire Records – particularly as it’s been five years since their last record due to a change in line-up, with Emma Smith replacing Stephanie O’Brien in 2012.

“We wanted to give ourselves enough time to really own our sound again. We never lost it but a new member always changes the sound so we wanted to know exactly what it is again,” says Puppini, who lives in Bethnal Green.

Despite only just releasing the album and a deluxe edition containing electro-swing remixes coming out in September, the group have already started planning ahead. Next up, they have their sights set on an all-originals record.

“It’ll be a challenge,” admits Puppini. “When you’ve started out by covering classics, you’re putting yourself up there with the greatest composers who’ve ever existed, so the pressure is high.

“But we’ve made five albums so we’re getting to know ourselves more, so now I think it’s time to take the plunge.”

When I ask if there’s any chance of another Bublé collaboration, Puccini gives a tantalising answer.

“I don’t know yet. We were thinking – but I don’t know if I can say. But we would love it if we did.”

My advice would be to watch this space.

The Puppini Sisters perform at Islington Assembly Hall on May 18, tickets.