The following brief history of the band is intended to hit the major points, without being exhaustive. Dr. Feelgood, formed in 1971, consisted of Lee Brilleaux (vocals), Wilko Johnson (guitar), John Sparks (bass) and The Big Figure (drums). That lineup recorded four albums (including one live one). When they were working on the fourth album, the band had a dispute over song selection. Wilko didn't want the song "Lucky Seven" included, and threatened to quit if it was. It was and he quit. As an aside, I'll note that I think this was really over more than just the inclusion of one song. I haven't interviewed anyone, or read this opinion expressed anywhere, so I have no evidence for saying it, and it is strictly speculation. But Wilko and Lee were essentially co-frontmen for the band, and I suspect the row over "Lucky Seven" was really a symptom of a simmering power struggle. I get the impression that that one of them would have left sooner or later, and that dispute, while being the proximate cause,was simply the straw.
At any rate, Wilko's departure was a big blow to the band. A lot of their sound was built around his choppy guitar style, and he did take lead vocals on a few tracks. Here is a clip of the the original lineup performing "You Shouldn't Call the Doctor (if You Can't Afford the Bills)":
Many predicted the band couldn't go on without him, but they did. Wilko was replaced with Gypie Mayo and continued on. Here's a video of the second incarnation (i.e., with Gypie on guitar) doing "Milk and Alcohol":
The new lineup was stable for several years, but Gypie eventually left and was replaced. There were a bunch of personnel changes over the years, and (through 1994) one can almost think of Dr. Feelgood as Lee Brilleaux and whatever musicians are playing with him. Now that's a slight exaggeration, since the lineup that Lee put together in March 1983 stayed together for more than half a decade. Following is a clip of that lineup doing "Don't Wait Up" from album Brilleaux:
Of all these changes I think the most significant was the first one, when Wilko left and was replaced by Gypie. As I noted, the band's sound was built around Wilko's choppy guitar style. Gypie was, I think, a better technical guitarist, but Wilko's style was distinctive. He often sounded like two guitarists, playing both rhythm and lead simultaneously. He explains it in this clip:
So that lineup change led to the most radical change in the band's sound. Also, Wilko sang lead on a couple of tracks (though now that I look back over the early albums, I realize that he sand less than I thought). But most importantly, his departure left Lee as the undisputed frontman.
At any rate, Lee died of lymphoma in 1994. Normally his death would have marked the end of the band. But it was Lee's wish that the band should continue, so in 1995 drummer Kevin Morris (who, at Lee's death was the second-longest-serving member of the band, having been in since 1983), guitarist Steve Walwyn (who, at Lee's death, had roughly five-years' tenure) and bassist Phil Mitchell (who had been in the band from 1983 until 1991) got back together, hired Pete Gage, and put out the cleverly-titled On the Road Again. Pete was then replaced by Robert Kane. The current lineup is still touring, though their last (most recent?) album came out in 2006 (Hey, guys, give us more. Please.). Following is a clip of the current lineup doing "Back in the Night," a song which was originally recorded by the original lineup (on their second album, Malpractice.):
But there has been continuity. Also Lee wanted the band to continue, and as near as I can tell, they have stayed loyal to his vision.
So I look at it and say, yes. It's the Doctor.
Lee Brilleaux, 1952-1994. RIP.