The conversation, such as it was, progressed with the man with the guitar asking Reilly if she fancied doing some songs with him. "When?" she asked. "Now," he replied. "But I don't know your stuff," she said. And thus, with a run-through of all the songs in that evening's concert and a lot of scribbling, Reilly there and then joined Mike Oldfield's band, making her debut in Dundee with the stage at her feet covered in those scribbled lyrics.
Despite their awkward meeting, it was to be the beginning of five successful years for Reilly and Oldfield in the early 1980s, with hits including Moonlight Shadow and one of their songs, Family Man, being taken to the American Top 10 by Daryl Hall and John Oates, one of innumerable excuse-me-while-I-pinch-myself moments that crop up in conversation with Reilly.
As she takes a break from recording her latest solo album and preparing for her Celtic Connections debut, the former singer with 1970s Glasgow soul-funk band Cado Belle fires off anecdote after anecdote. There was the time Cado Belle – who had become a kind of house band at the Third Eye Centre in Sauchiehall Street through rehearsing in one of its draughty, leaky rooms – found themselves collaborating with avant garde composer Karlheinz Stockhausen. "Very bizarre," recalls Reilly.
When Cado Belle lost out in punk rock's takeover of the record business after just one acclaimed album, and once the Mike Oldfield Band had spilt, a more instantly appealing collaboration saw Reilly, recording in a huge castle complete with overhanging cliff outside Cologne with Jack Bruce, Ginger Baker, Clem Clemson, Gary Moore and others. She would go on to write and perform with the Berlin Opera Company, share a table in Los Angeles with one of the legendary Holland-Dozier-Holland songwriting team when her Everytime We Touch, a hit across Europe and No 1 in Norway, was honoured at a music industry dinner, and take a call from Jack Bruce's songwriting partner, Pete Brown, talking her through the lyrics to songs she was to sing on the former Cream bassist's Somethin Els album.
"I remember speaking to Pete Brown, thinking, 'this is one of my heroes on the phone', and saying to myself afterwards, 'I love my job'," she says. "But that's happened so much and it still happens. The other day in the studio, Ross Hamilton, the bassist who's working on my new album, sang a vocal and I thought, 'Yes – you can do the whole album and I'll just enjoy listening to you instead of singing myself'. But then the other musicians come in, like the piper and whistle player Jarlath Henderson, who's done a brilliant solo, and Duncan Chisholm, who has a gorgeous touch on the fiddle, and I want to sing with them."
The new songs she's working on with her long-time musical partner, Cado Belle keyboardist Stuart Mackillop (who worked with Abba after the Scots band split), continue the Cado Belle style of soul music mixed with Scottish melancholy, hence the appearance of Henderson and Chisholm, two of the most soulful players on the traditional music scene. Not that Reilly's a stranger to folk musicians, as the Finnish vocal trio Vaartina are among her other past collaborators.
She has, though, been a bit of a stranger to the Glasgow live music scene, despite living in Bearsden and recording regularly in the city, and her Celtic Connections appearance is just one of a handful of live gigs she has performed here over the past 20 years.
"I still feel a real affinity with Glasgow," she says. "Because it's my home town and although I've worked a lot abroad, especially in Germany, I've never lost touch with the people I grew up with musically. I still see or speak on the phone with all the guys, musicians and sound crew, from Cado Belle. We were always like a family."
They even had a family pet, Dill the dog, who went on to play a cameo role in one of the late Michael Marra's greatest songs, Julius, which was written from the perspective of another canine with musical associations, the put-upon old English sheepdog companion to Dougie Martin of Dundee band Mafia.
"I'm promised heaven but I'm given hell," sings Julius as he's banished again to the car during a gig, "when I think about that mongrel on the stage with Cado Belle."
"Oh no, that's brilliant," says Reilly. "That completely passed me by. I must go and find it."
Maggie Reilly plays the Tron Theatre, Glasgow, on January 27.