The Webb Sisters have struggled not to be mentioned in the same sentence as Leonard Cohen over the past few years, after playing with him on his world tour. As the Kent duo play their own concert in their home county, Chris Price discovered their other star connections.

It seems not a day goes by without another scantily-clad scandal involving the latest pop princess, which should mean there is little space in the music industry for an act like the Webb Sisters.

Demure, softly spoken and with a tendency to leave long pauses before they speak, this timid pair appear lost in the music world – until they start to sing.

Their sweet harmonies caught the attention of Leonard Cohen four years ago, who wasted no time in bundling the Sevenoaks-born siblings on to a plane to join him on his world tour.

In the middle of recording their third album at the time, Leonard’s call in early 2008 meant the duo had to finish the record in fits and starts on the road. They played with the Canadian singer-songwriter from May of that year to Christmas 2010 and headed to the studio whenever they had time off.

Eventually, Charley and Hattie released their third record, Savages, in May 2011. It had been more than three years from beginning to finally touring last summer. Now on their second UK tour, they are revelling in its overwhelmingly positive critical reception.

“It has been better than we hoped,” said Charley. “I am not sure what expectations we had. We just wanted to make an excellent album which came authentically from where we were.”

The record was co-produced by Peter Asher, who also manages the duo from his LA base. Something of a recording legend, Peter has produced albums for Diana Ross, Cher, James Taylor and Neil Diamond since becoming a star in the 1960s as part of vocal duo Peter and Gordon.

Attracted by the girls’ harmonies, Peter allowed the recording process to be very informal. On some tracks the sisters wrote the song the day before they went in the studio, thought about what instruments they were going to play when they arrived, and sent the track to LA for Peter to add a bassline and do some mixes.

Charley, 32, said: “We are very lucky with the digital age to have been able to listen to things as Peter was mixing them, even though we were on the other side of the world.”

Chatting on a train as they prepare for the opening night of the tour, both sisters are calm and unfazed by the superstar connections they have fostered. Sting invited them to sing on his 2009 album If On a Winter’s Night… and they have toured with Jamie Cullum, James Morrison and Katie Melua. Yet they are indifferent when it comes to the question of fame.

Hattie, 30, joked: “We share a room on our tours, unlike touring with Leonard Cohen, where we get our own room.”

The girls took pride in being involved in every aspect of making Savages, from the recording to the artwork and photography on the album cover.

Hattie said: “It is very interesting when people choose to get involved in the whole gesture of creativity and when an artist has a thread running through all their work,” before confirming “that’s what we do” when asked if they come under that category.

Charley added: “I have never paid attention to being famous or not. If we had set out to be famous we would have taken a different artistic route. We have only ever taken steps forward that have allowed us to make the music we enjoy.”

Charley and Hattie Webb are working on a new record and have started playing some new songs at gigs, with plans to get into the studio in the next couple of months.

They aren’t averse to the idea of putting out another EP first, as they did with The Other Side in 2009 before releasing third album Savages.

“It means we can put stuff out even if we are not quite ready for everything to go on an album,” said Charley, who was not as relieved as you might think at the prospect of making their next album in one place at one time, unlike their experience on tour with Leonard Cohen.

“There was an element on Savages of throwing stuff at the wall and seeing what would stick, but that becomes inherent when you are putting something together from lots of studio appearances.

“We had a certain spontaneity that enabled us to express ourselves in the studio. We didn’t wallow too much in our creativity.

“At the same time, making a record off the road will be an experience. I don’t know if it will be better or worse.”

The Webb Sisters will perform at St Mary’s Church in Sandwich on Saturday, February 11. Tickets £15. Box office 01304 611600.