Fran Alejandres has one listed on his site, however this may be the Ladbroke Sporting Casino (hard to tell from his list).

I found that there is a report published at http://www.gamingfloor.com/features/brit_gb/GB_97_98.htm that states...

At the end of March 1998 there were 119 licensed clubs of which 115 were trading. The total number has declined slightly but has been relatively stable for the last 20 years. (Subsequent to the report being published the Rotunda in Glasgow as well as the Ladbroke Sporting Club in London have had well publicized openings)

I wonder if it is still open, I did find a listing for the Ladbroke Sporting Casino in London with an address and telephone number.

Plus an article at http://www.lvrj.com/lvrj_home/1997/Aug-13-Wed-1997/business/5876777.html that states (Aug 13 1977)...

The British company -- which already operates four London casinos, including Maxims and the Barracuda -- said it will open the Ladbroke Sporting Club, a 10,100-square-foot casino aimed at lower-stakes gamblers, next summer.