Previous to UK soul superstar James Hunter’s latest release, The Hard Way, his connections to New Orleans were 1) A YouTube video featuring him as Howlin’ Wilf doing Lee Dorsey’s “Ya Ya;” 2) Watching the aftermath of Katrina on the BBC; and 3) Hiring New Orleans’ Derek Huston to play baritone sax on portions of American tours.

Now add Allen Toussaint, who guests on The Hard Way.

“It was a minor miracle getting Allen,” Hunter says. “Allen came to hear us in...