After falling in love with rockabilly and the blues as a nine-year-old in Dublin, May has turned the genres into a swinging fusion of both classic and modern.
Her album Love Tattoo gives a nod to the retro while retaining a fresh sound.
A couple of months after spotting her play live, Holland invited her onto his show, with May finding herself playing alongside Jeff Beck, Elbow and Roots Manuva.
"It's all gone mental lately," she explains.
"I've got a huge tour lined up and Elbow want me to do a track on their next album, as a result of Later."
May had been selling her album at gigs before Universal Classics came on board.
"We'd only been selling it at our shows – it's great to actually have it properly released," she explains.
"It only took us eight days to record it. I get bored easily and wanted to keep everything very fresh and capture the vibe of the performances.
"We're already working on a new record. It will be a bit heavier with more guitars and trumpets.
"I'm very happy with how it's going and I hope it will be out some time this year."
In the meantime, May and her band are concentrating on a UK tour which is already under way and will see them play about 36 shows in 38 days, which includes a gig in Northampton this month.
May is the youngest of five children and, living in a two-bedroom home, there was no avoiding the music her older siblings listened to – a combination of folk and the usual chart pop, but there was also Elvis.
"My brother was a mad Elvis fan, and I found a tape in his room with Elvis, Eddie Cochran and Gene Vincent. I thought the music was fantastic," she explains.
May had discovered, aged four, that she had a singing voice by harmonising with her sister's folk band.
Her tastes developed, along with her fashion sense, and she got into Elmore James.
"Then I heard Billie Holiday and that blew my mind," she says. "My brother took me to HMV and I bought my first Billie album."
After a year of art college, Imelda realised she'd rather sing for a living.
She gigged at Dublin's Bruxelles club, where she was occasionally barred from her own shows for being underage.
In 1998 she decided to try her luck in London and quickly got work with renowned rock 'n' roller Mike Sanchez and swing troupe Blue Harlem.
"We did a lot of corporate things where I had to look 1940s, with a red satin dress and a flower in my hair, but I really learned to scrub up and get my act together," she explains.
By 2006 she was itching to go solo, and formed her own band.
After being spotted by Jools Holland she was invited to support his band before appearing on his radio show and his BBC2 show.
"It was quite unbelievable. I was very nervous and happy," she explains. "I got the call two days before the show.
"It was really strange to be somewhere you see on TV so often."
The Irish World Newspaper Awards crowned May best female newcomer last year and she has also been nominated for the best female award at this year's Irish Meteor Awards, up against Tara Blaise, Lisa Hannigan, Gemma Hayes and Camille O'Sullivan.
"To even be nominated is fantastic," she says. "I couldn't really believe it, it feels great to get a pat on the back, considering where I feel I am in my career."
Imelda May plays the Northampton Roadmender on Saturday, February 21.
Tickets cost £10 and doors open at 7pm.
For more information visit www.imeldamay.com.