The De Luxe Blues Band:

Blues band formed in the 80's by veteran bassist Bob Brunning, previously working with Brunning Hall Sunflower Blues Band and short periods with Fleetwood Mac (their first bassist) and Savoy Brown. Through the years, the De Luxe Blues Band has often been featured as back up band for U.S. blues singers/guitarists touring the U.K.
The 'original' De Luxe lineup:

Daniel 'Danny' Adler: guitar, vocals

Bob Hall: piano

Bob Brunning: bass

Mickey Waller: drums
Guitarist Danny Adler came from U.S. band The Roogalators. Played the blues on a vintage Fender Jazzmaster: not the most common of blues tools.
Check out the Roogalator album "Play It By Ear", originally issued on DO IT RECORDS, RIDE 1 (1977). Not a blues album at all - probably labelled 'new wave' at the time. Good cut: "All Aboard" (once a single). And the album cover features the Jazzmaster!

The 1988 album "The De Luxe Blues Band" (cover above) features as basic band lineup:
Al Vincent: guitar (also with Shakey Vick)
Dick Heckstall-Smith: saxophone (ex-The Graham Bond Organization, Colosseum etc.)
Bob Brunning: bass
Mickey Waller: drums
Phil Taylor
Dave Beaumont
According to Pete Farrugia, Oct. 98:
"Bob Brunning has a new line-up of the De Luxe Blues Band. He also runs a Blues club called BB's in Merton, South London every Sunday night."
Very true. The line up, quoted from The Colour House Theatre's (the current address for BB's) website:
"Bob’s own band in it’s fourth incarnation. Russel Baillie on vocals is a fantastic front-man guaranteed to get everyone dancing (check out his vocal on live favourite track ‘I Know’). Bill Smith is an accomplished harp player, joined on stage by his guitar-prodigy son Dan (Smith). This young man is one to watch. Reg Patten’s superb drumming is perfect counterpoint to Bob’s bass duties. The sextet is made up by Dennis (McGrath) (standout solo on Peter Green’s ‘Have you ever loved a woman’). If you’ve never seen this band then you really should make your way to SW19 for a Deluxe evening."
Guitarist Dan Smith left the band late Nov. 2000 in order to work with Marcus Malone and jazz/rock/funk band Sonarfly.
Lineup late 2001:
Russel Baillie: vocals
Bill Smith: harmonica
Dennis McGrath: guitar
Bob Brunning: bass
Reg Patten: drums
"Live At Half Moon Putney " VIRGIN (1981)
"A Street Car Named De Luxe" APPALOOSA AP 020 (1981)
"Urban De Luxe" APPALOOSA AP 040 (1983)
"Motorvating" APPALOOSA (1988)
"The De Luxe Blues Band" BLUE HORIZON 004 (1988)
(number 6)
"The De Luxe Blues Band" BBCD4 (2001) on BB's Records, his own label