Bear-like of body, voice and beard, Nathaniel Rateliff and his band the Night Sweats have attracted a broad audience in admiration of their Stax Records-released, self-titled debut album. Gig-going old-timers, male and female alike, rub shoulders – quite literally in a sold-out Stereo basement – with others who look young enough to be first-timers. If this seven-piece from Denver, Colorado, did weddings, they’d probably never want for steady work again.

The universality of their appeal is down to a style of rootsy, gospel-infused Memphis soul that surely no one could profess to hate. The sort of snaking basslines, thumping beats and purring organ and horns that colour openers I Need Never Get Old and Look It Here will always find welcoming ears and feet so as long as Sam Cooke, Otis Redding and Sam and Dave et al remain in favour.

Dabbing his brow with a handkerchief beneath a black fedora, Rateliff has a hint of the fiery backwoods preacher man about him, but nevertheless cuts a mild figure, at ease as a bandleader after years of toiling as an unspectacular alt-folk soloist. Trumpeter Wesley Watkins may dance like he has ants in his pants, but Rateliff and the Night Sweats’ music doesn’t inspire raptures so much as a medium-watt feelgood glow. There are shades of Graham Parker and the Rumour about the sweetly swaying Howling at Nothing and I’ve Been Failing. Trying So Hard Not to Know comes on like Van Morrison riding a runaway train.

In a frenzy of foot-stomps, handclaps and wordless woah-woahing, during which Rateliff thirstily howls “son of a bitch, give me a drink”, their hookiest song SOB refuses to quit. After a fake ending, the chorus comes back by popular demand. Then bookending a cover of the Band’s The Shape I’m In, SOB is back again for a last go-around, the crowd woah-woahing Rateliff and co off stage in a town where they need never want for a drink again.

• At Belgrave Music Hall, Leeds, on 2 October, box office: 0113-234 6160; CLF Art Cafe, London, on 3 October, box office 020-7732 5275.