Before Amy Winehouse said no, no, no to “Rehab,” before Duffy begged for “Mercy” and before Adele sang about “Chasing Pavements,” there was Sharon Jones & the Dap-Kings.

Though the Brits had more mainstream success reviving the sweet sounds of ’60s soul, the Augusta-born Jones and her backing band have been doing it longer, forming in the late ’90s and releasing two critically acclaimed albums before 2006’s “Back To Black” put Winehouse on the map. If there’s any justice in the world, Jones’ new album, “I Learned the Hard Way,” will bring her the breakthrough success she deserves.

It’s been a long time coming: Jones, who turns 54 in May, started out singing in church, developing a soulful, gospel-influenced sound that recalls legends such as Mavis Staples, Aretha Franklin and Marva Whitney. In high school she fronted various funk bands in her neighborhood, but signs suggested she might never become a star.

“By the time I hit my early 20s, they told me I didn’t have the right look: I was too dark, too fat, too short,” she recalls matter-of-factly. “But I kept thinking that God had given me a gift, and that one day people would accept me for my voice rather than the way I look.”

To make ends meet, she worked as a corrections officer at New York’s Rikers Island and as an armored car guard for Wells Fargo. But her life began to change in the mid-’90s when she met the future Dap-Kings, former members of hip indie bands such as Antibalas and the Soul Providers.

“I was still singing in a wedding band until I met them, but once we started going to Europe on tour, they had to replace me,” she says. “The Dap-Kings would be making $50 a night and coming home with no money, and I’d be turning down $500-a-night gigs with the wedding band! But I had to make that move.”

The group got a huge break when the Dap-Kings were hired by producer Mark Ronson as Winehouse’s backing band for “Back To Black,” which sold more than 12 million copies and was widely considered the year’s best album. But Jones remains rather circumspect about the impact it had on her band’s career.

“Even though the Dap-Kings played on it, it was Amy and Mark’s music,” she insists. “It was good exposure for Daptone as a record label, but Amy never gave props to us. I knew we’d inspired her, because when we started going to England there wasn’t anyone doing what we were doing. The next thing you know, you’ve got Duffy and Adele following in her footsteps, but we were the first!”

Fortunately, what goes around eventually comes back around. In 2007, Jones was tapped for a role in Denzel Washington’s film “The Great Debaters,” playing a juke joint singer and contributing covers of several 1930s songs to the soundtrack. She was invited to sing with Lou Reed and Booker T & the MGs, and in 2009 she performed a historic show with reunited jam-band icons Phish in which they performed the Rolling Stone’s “Exile on Main Street” in its entirety. This January, Jones sang a duet of “Baby (You’ve Got What It Takes)” with Michael Bublé on “Saturday Night Live,” and she clearly remains a fan of the crooner.

“Michael reminds me of that swinging ’60s vibe, so we’re influenced by the same era of music. It was great exposure for me!” she says with a boisterous laugh. “I don’t know what the future holds, but I hope it will bring more good things. I just want to share the gift God gave me and show people that you shouldn’t give up after 40. You’ve got to keep going!”

Jones and her Dap-Kings will continue to do just that with the impending release of their fourth album. The group is preparing for its biggest promotional onslaught to date, playing various talk shows and touring tirelessly. But Jones, who possesses the infectious enthusiasm of a woman half her age, seems more than ready for the task, energized by working with musicians she truly admires.

“[The Dap-Kings] write the greatest songs, and sometimes I just sit back and watch them,” she gushes adoringly. “They amaze me! We recorded our new album months ago and I had copies of the rough mixes, but when I got the final version, I listened to it for the first time from top to bottom while at a photo shoot. I was like, ‘Wow!’ I got so into it, I had to stop myself before I got a big head!”