When the Beatstalkers play the Arches as part of Celtic Connections this weekend they'll be expecting a crowd.

The Beatstalkers always expected a crowd. At one point the band's mere arrivals and departures by train could draw hundreds of fans to Glasgow Central station. Even they were taken aback by the news that reached them in their manager's office one lunchtime in the 1965 that thousands of people had gathered for the free concert they were about to play in the city's George Square.

The gig in question has gone down in Scottish pop history as a kind of forerunner to the Rolling Stones' infamous Altamont experience, thankfully without loss of life but with Glasgow gang the Tongs acting as "stewards" – as the Hells Angels did at Altamont – and the stars of the show managing to escape to gig another day.

"These were wild days," says Alan Mair, bassist with the Beatstalkers who went on to sell boots to pop music's those and such as those (one Freddie Mercury was his sales assistant) before forming The Only Ones during the 1970s punk era. "We were friends with the Tongs because another gang, the Maryhill Fleet didn't like it when their girlfriends became interested in us. So we'd have these bodyguards travelling with us in our van and all sorts of mayhem going on, really wild scenes at gigs and outside venues."

For about a year before the George Square riot, the Beatstalkers had been building an audience throughout Scotland for their blue-eyed soul and rhythm and blues. Every gig in every city and town would be sold out and when their manager made contact with the Moody Blues' manager, John Fenton, and Fenton duly arrived in Glasgow with the Moodies' record producer, Denny Cordell, in tow, it seemed a foregone conclusion that the Beatstalkers' popularity would transfer automatically to the wider market.

They set off for London, where they quickly established a successful residency at the Marquee club, but their record company, Decca, and management steered them towards a different kind of song to the ones they'd built their success on in Scotland.

"We wanted our first single to be Nina Simone's Gin House coupled with The Tams' Hey Girl Don't Bother Me because we'd played them live and we already had strong versions of them and they were going down well with our fans," says Mair. "But we were told that original songs, specially written for us, was the way to go and I suppose it was the classic case of a naïve band being led by people who'd had success in the business."

Other factors were against them. One single, Everybody's Talking About My Baby, says Mair, actually sold 200,000 copies in Scotland alone but at the time only two shops in Scotland registered sales for the charts and the Beatstalkers stalled at Number 37 when, on sales, the record would have reached the Top 10. A change of label, to CBS, and songs from an emerging star in his own right, David Bowie, didn't change their fortunes and towards the end of the 1960s they went their separate ways professionally, although they remained friends.

A retrospective CD and a reunion gig at the Barrowland Ballroom in Glasgow in 2005 showed them that interest in the Beatstalkers remained keen and the band enjoyed getting back together.

"I'd kept in touch with everybody except Eddie Campbell, our piano player, but he heard about the CD coming out and got in touch, and when we got together to play, it was like old times," says Mair.

"The guys in the band are probably my oldest friends. I went to school with Dave [Lennox], our singer, and I'd always see Ronnie [Smith, guitar] when I was back in Glasgow, and there's a really good feeling when we all meet up. It never really bothered us that we didn't make it bigger and we weren't disappointed in the end because we didn't fail on our terms. If we'd failed with songs we'd chosen, instead of songs that were chosen for us, we might have beaten ourselves up a bit."

For their Celtic Connections gig, the band will be without Campbell, who had a gig of his own he couldn't get out of, but they'll have British R'n'B legend Zoot Money, with whom drummer Jeff Allen works regularly, on keyboards in his place. They also have a brass section and backing vocalists, so it's a bigger show than the gigs they played in the 1960s.

"We're really pleased to be playing in the Arches," says Mair. "Because it'll feel like a club gig and it'll be a bit like Le Cave, which was just round the corner underneath another set of arches and was the hip gig to play back in the day. Alex Harvey's Big Soul Band, Blues Council, bands like that all played there – and eventually so did we. So although we've never played the Arches, it'll still be like being back in an old haunt."

The Beatstalkers play the Arches on Saturday with Hamish Stuart of the Average White Band.