Image copyright Jory Lee Cordy Image caption Drax Project (L-R): Sam Thomson, Shaan Singh, Ben O'Leary and Matt Beachen

If Shaan Singh hadn't forgotten his wallet, he might never have played with Ed Sheeran.

Two years ago, the singer left a late-night rehearsal with his band, The Drax Project, intending to catch the last bus home.

But when he got to the stop, he realised he'd left all his money at his bandmate Ben O'Leary's house. Sheepishly, he returned to ask if he could crash for the night.

"I remember Ben was really angry with me," he says.

"It was Saturday night at 12 o'clock!" O'Leary exclaims. "I'm not generally that angry but I wanted to go to bed!"

Instead of going to sleep, though, the duo started mucking around on the guitar. Twenty minutes later, they'd written the verse and chorus of a new song - Woke Up Late - a fizzy, frisky pop anthem where Shaan rolls out of bed after a big night out, liberated from his wallet, but sitting next to "a girl that I had hardly met".

A sleeper hit, it's been streamed more than 57 million times since its release in 2017, winning single of the year at the 2018 New Zealand Music Awards, and eventually hitting the US charts this January after actress Hailee Steinfeld jumped on a remix.

The song's success also earned the band support slots with Lorde, Camila Cabello and, yes, Ed Sheeran.

"Ed was such a lovely guy," says O'Leary. "He took us out for dinner after the show, and spent 30 minutes talking to us, giving us some of his wisdom.

"He's a big inspiration. Refining our writing to get to his level is definitely a goal."

The band have certainly made huge strides since they started out busking cover versions on the streets of Wellington. As they release their new single, All This Time, the band explain how it all happened... and why it cost Shaan his career as a "speed-cuber".

Woke Up Late has been out for two years now, and people are still picking up on it. How do you explain its longevity?

Shaan Singh [vocals / saxophone]: It's really hard to pinpoint [but] I guess it's just the song? Maybe it's just a story that's super-relatable?

Ben O'Leary [guitar]: There's no tricks to the song. It's a simple melody, simple lyrics and a really easy-to-follow story. There's no big metaphors or anything. It's really literal.

Shaan: It came together quicker than any other song we've written.

Ben: Up until that point, we had quite an unrefined process of writing - but I think the speed at which we wrote Woke Up Late ended up giving the song that natural feeling. So it really helped us as writers.

Have you had to sit on your hands while the song takes off?

Ben: We do have a lot of music that we've written since then that we're waiting to release, eagerly.

Shaan: We're still finishing some of the songs, but we're excited to release an album this year.

Tell me how you started off… You were music students, is that right?

Matt Beachem [drums]: Yeah, we were studying jazz together. Sam, Shaan and myself, and Ben was down the road at another music school.

A rival music school?

Matt: Fights on the streets! Nah, it's all peace and love. But about five years ago, we decided to go busking in the party streets of Wellington. So it was Shaan and I on drums and sax, which becomes "Drax" and we were playing covers: Cry Me A River by Justin Timberlake, classic Stevie Wonder, Thrift Shop by Macklemore. Anything to get people's attention.

What made you the most money?

Matt: Thrift Shop - because it had that awesome sax riff. There's a YouTube video that went, I don't know if you could call it viral, but it got like 12,000 views.

Ben: That's New Zealand viral.

What was the transition from busking to being an actual band?

Shaan: Bar managers would walk past us and say, "Hey, come and play at my bar tonight". So we got that going, did that for almost a year. During that time we added Sam and Ben on the bass and guitar and started writing our own songs.

Since then, you've toured with lots of big names. Who's been the biggest inspiration?

Shaan: Camila Cabello showed us how to work hard. She does three-hour meet and greets before every show.

Sam: Ed Sheeran hired all his childhood friends to be his crew and I thought that was amazing.

Shaan: Our team is actually really close. We've been with our manager since we were busking. He gave us 20 bucks, and we've been with him ever since.

Has he seen a good return on that investment?

Shaan: I think he's still waiting - but give it time!

Shaan, you have an incredible falsetto on the new single. Do you have any special techniques for hitting the high notes?

Shaan: Haha, the vocals do go a little high in that song! Maybe playing the saxophone helps.

How did you come up with the saxophone drop? It sounds like nothing I've ever heard.

Shaan: We came up with the saxophone drop together, actually. I remember us thinking at the time, 'Is this a little too ridiculous?' and we all agreed it was. But we like it that way.

Image copyright Getty Images Image caption The classically-trained band mix elements of jazz, funk, R&B and pop

Shaan, is it true you can solve a Rubik's Cube in under a minute?

Shaan: Yeah, I can - but I haven't done it for a couple of years.

Sam: Last time you did it, it took 37 seconds I remember.

Shaan: I need to practise more. I'm nowhere near that now.

Sam: What's your fastest time?

Shaan: My fastest is like 20, 22 seconds.

What's the world record?

Shaan: It's like four seconds. An Australian guy, Feliks [Zemdegs]. I met him, he's the man.

Was that your big passion before music? Did you go to conventions?

Shaan: I did go to the New Zealand championship when I was 16.

Ben: What the hell? I didn't know that!

Shaan: It was really fun but those days are behind me.

Sam: You're really good at honing in on specific things and focusing all your energy on them.

Ben: You're also really bad at losing, so it's probably for the best you gave up.

Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.