A COUPLE of years ago, Stuart Murdoch, singer and founder member of Glasgow’s Belle and Sebastian, told a lovely little story about a young couple who attended a London show by the band.

The man contacted the band to say his girlfriend had secretly bought tickets for the show - something he had only learned because she talked in her sleep - and asked if he could propose to her on stage just before the group sang her favourite song, Piazza New York Catcher.

Murdoch duly got the couple up on stage - the woman still unaware of what lay in store - and, just before he began the song, he asked the boyfriend: “Have you got anything else you’d like to say?” The proposal was made and his girlfriend burst into tears. “I knew it would be overwhelming”, Murdoch recalled, “so I thought we would just launch into the song while they discussed it … The answer was ‘yes’, though”.

An unusually open and accessible band in all sorts of ways, it was typical of Belle and Sebastian that they were more than happy to accommodate the young couple. The band pride themselves on accessibility. Murdoch himself tweets regularly: offbeat observations, political opinions (Brexit, for example, is “an excuse for the worst sort of pseudo imperialistic bullshit”). Last November, in the Diary section of the group’s website, he wrote about his wife, Marisa, giving birth to their second son, Nico Robert Salvatore. And there’s a Q&A section on which fans can ask the band members all sorts of questions.

The band, who round off the BBC 6 Music Festival tonight at the O2 Academy, have worked their way into the hearts of fans with a succession of well-received albums that began, back in June 1996. After unsuccessfully trying to put a band together, Murdoch met Stuart David (“a kindred spirit”) on a music course for unemployed people and they recorded some demos. One of them was taken up by Stow College, which each year put out a record to aid students aiming to make it in the music business.

“They picked my songs for this college course and we made our first record," Murdoch said. “It was that that became a catalyst for suddenly meeting all the rest of the members of the band. That happened quite quickly, and it was overwhelming, and it was terrific.

“After seven years of nothing happening, suddenly all these people came out the woodwork to record this record. I met Stevie [Jackson], Isobel [Campbell], Chris [Geddes], Mick [Cooke], all within a short period.”

The debut album, Tigermilk, released via Stow College’s Electric Honey label, was followed by acclaimed If You’re Feeling Sinister (1996), The Boy With the Arab Strap (1998), and Fold Your Hands Child, You Walk Like a Peasant (2000).

This was a real purple patch for the band - named after a classic French children's TV series from the 1960s - and its literate, sophisticated storytelling. If You’re Feeling Sinister is often seen as their masterpiece. Rolling Stone magazine said it “stands in stark contrast to much contemporary pop for a couple of reasons: not only is it unabashedly gentle, but the album is completely narrative driven. All the songs have the smooth flow of good storytelling … [The band] reaches peaks of effortless pastoral grandeur”.

The music writer Malcolm Jack, looking back, on his favourite album, wrote of it: “Subtly poetic, wickedly funny, gorgeously melodic, steeped in ramshackle C86 jangle and the pop classicism of Bob Dylan and the Velvet Underground, it encapsulates everything I've come to treasure in music.”

To their fans, they are beloved - poetic, witty, mournful, a sort of distillation of the best qualities of the modern Scottish soul; to their detractors they are so achingly hip they set their teeth on edge.

The band has had a number of line-up changes over the years but has continued to deliver a series of highly literate and highly enjoyable albums, including Dear Catastrophe Waitress (2003), The Life Pursuit (2006), Write About Love (2010, with Norah Jones and Carey Mulligan as guest vocalists) and the most recent album, Girls in Peacetime Want to Dance (2015). Along the way there have been compilations and EPs; and Murdoch himself directed a fine film, God Help the Girl.

Since 1996, they have, as the music critic, Laura Barton, says “quietly become one of the UK's most popular bands, adored for their exquisite pop sensibility and lyrics that not only owned a kind of tragi-comic precision but that were also sharply, sorrowfully beautiful”. Another critic has described them as one of the world’s biggest cult bands.

They have toured frequently - Europe, the US, Japan, Australia - and they will be hitting the road again this summer, with a string of dates in North America. They also play Glasgow’s TRNSMT festival on July 7.

Looking back on his time with the band, Murdoch himself said in 2015: “The first three or four years were tumultuous. We were still finding ourselves and we made all our early records, probably the records that we are best-known for. But it wasn’t until 2001 that we started touring the world with our crew … and suddenly everything started making sense, and this experience of going out and playing concerts all round the world became possible and completely enjoyable.”

The memory of a pivotal gig in Dunoon has never quite left him. “We were doing our rehearsals there and every morning we got the ferry over. I’ve got this thing for ferries, and I just thought, ‘This is great, we’re getting a ferry to work, to do a concert that night, and we’ve got string players along’, and everything just fell into place. We never looked back after that.”