A sign of getting famous is clearly when other pop acts start sneaking notes into your hotel room asking to see you.

Sadly for Ed Sheeran, the offer on the table was not quite as glamorous as it might initially sound, although it might reap dividends on the BRIT award winner's second record.

"I played in a stadium with Lenny Kravitz and Snow Patrol in Switzerland, and Gary Lightbody slipped a note under my door later on saying he was a big fan and asking me to come and have a pint with him," recalls Sheeran with a chuckle.

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"He was like, we'll be touring America for three months, do you want to come on tour with us? I did that, and we struck up a really good friendship with them as they're really lovely lads. I wrote about five songs with Gary and Jonny [Quinn, Snow Patrol's drummer], so that might be on the next album."

Sheeran comes across as a rather modest and down-to-earth individual, relating these stories with a laconic air. He's doing well to be so relaxed, given that his sophomore record will be under close scrutiny. His debut, 2011's +, catapulted the unassuming 21-year-old to sudden pop stardom.

While Sheeran had been a regular on the gigging circuit for some time and had built a devoted fanbase, the sheer scale of his success remains surprising, especially given his unlikely musical merging of acoustic guitar and grime rapping. The latest stop on his success ride comes next week, with a sold out gig at Edinburgh's Usher Hall followed by a three night stint at the Barrowland Ballroom in Glasgow. While he currently has 24 songs written for his next record, he's not planning on giving any of them an outing yet.

"I'm wary of dropping in new material until I've decided what's exactly going on the next album," he explains. "But I'll be playing some older songs that I've not played live before. My job as an entertainer is to entertain, so I don't want to indulge myself too much by playing all these new songs that people won't know.

"They're the ones who are there to enjoy it and two hours of new material, there's some people that would enjoy it and a lot that wouldn't at the moment."

He takes a similar approach when considering what will go on the album itself. While he doesn't seem keen to merely repeat +, it seems unlikely he'll be stretching the boundaries too far, either.

"I think the trick with the second album is to not go too left of centre but not be totally the same," he says. "I'm not going to be bringing out some Tibetan monks to sing on it and it won't be the same lyrically as the first one either.

"There will definitely be songs on there that will surprise people in terms of what I'm doing but it won't be a big mind warp to my fans."

Something that was perhaps a surprise was his duet with Taylor Swift on the pop starlet's new Red album. The collaboration, and the fact that Swift has now asked Sheeran to support her on a 2013 tour, has prompted speculation as to a romantic relationship, but Sheeran only focuses on how they hit it off as songwriters. "It's weird because in the music industry you spend 90% of your time sheltered from various things, so when you have common ground with someone you can strike up a good relationship with them in a very short space of time."

Sheeran seems to take most things in stride, including going from tiny venues to the likes of the Barrowland while still playing on his own without a backing band.

"Being dropped in at the deep end with a guitar, an effects pedal and being told you're playing Brixton Academy, that's really made me think about the live show more," he says.

"When you're playing to 200 people you can be intimate, but making a room intimate when you're playing to 5000 people is a bit tougher to do... I'm just very grateful that people want to come out and see me play live."

Ed Sheeran plays the Usher Hall in Edinburgh on Sunday, and the Barrowland in Glasgow from November 14 to November 16.