Sarah Jane Morris was 14 when she first encountered the music of John Martyn. 'I had watched the Old Grey Whistle Test,' she recalls, 'and I remember how beautiful his voice was. He was performing "May You Never" – and I had developed one of those teenage crushes because he was so beautiful – but his voice spoke to me. It was just such a beautiful, warm, chocolatey sound.'

Over subsequent decades, Martyn's music would become a backdrop to her own life as she developed as a singer-songwriter. With her new show Sweet Little Mystery, Morris celebrates the late Glasgow-born folk-rock genius through song, spoken word and filmed interviews. For several years, Morris – who found chart success in the 1980s with the Communards and has continued to plough an individual path through jazz, soul and R&B – has closed her concerts with Martyn's 'Don't Want to Know'.

'It's such a positive message, that lyric,' says Morris. '"I don't want to know about evil, I only want to know about love."' So when Morris found herself looking to take a breather from her own songwriting, a John Martyn project made perfect sense. Together with guitarist Tony Rémy, Morris started working on arrangements of songs from throughout Martyn's career. Thanks to her distinctive baritone vocal range, she hasn't had to change the keys.

'Having had my songs covered by other people, I know that you want them to show another side of it. Any good song can be changed in so many ways, and so we dared to do that, but we always did it with great respect.' The album features regular collaborators Tim Cansfield and Jason Rebello, alongside her old friend Eddi Reader, who sung with Martyn for the BBC's Transatlantic Sessions in 1999. 'It was just a lovely project to develop,' she notes.

The stage show is directed by comedian Mark Thomas, an old friend from the days of miners' strike benefits and Red Wedge. 'When he was starting out doing stand-up, I was in The Happy End, the big band. Me, Mark, Jeremy Hardy and Mark Steel all did the same circuit together. For the past five years I've been to see every one of Mark's shows at the Edinburgh Festival and they've been amazing.'

Morris doesn't want to give too much away about the show, but she does reveal that one of the filmed interviewees is the great singer Linda Thompson, who grew up with Martyn in Glasgow and moved to London at the same time. 'I met up with his lovely sister who had a whole other take on him,' adds Morris. 'I've become friends with Beverley, John's first wife, and you begin to piece together the man: a very complex character. But I think that "Solid Air", the song that he wrote to Nick Drake, has to be one of the most brilliant songs written in friendship to someone with mental health issues. I think it's genius. I don't think songwriting gets much better than that.'

Sarah Jane Morris: Sweet Little Mystery, Assembly George Square Studios, 2–11 Aug, 6.45pm, £13–£14 (£12–£13). Previews 31 Jul & 1 Aug, £10.