Oh, since you asked, but it gets complicated.
The original Communist Party of Great Britain (CPGB) was set up in the 1920s after the Russian Revolution through fusion of several existing socialist groups.
It never made much impact in elections, but did get a foothold in the labour movement.
The CPGB declined in the 1970s and 80s and the leadership tried to steer a more reformist course. People opposed to this walked out and founded the Communist Party of Britain (CPB).
When the Soviet Union collapsed, the mainstream CPGB, understandably enough, suffered complete political disorientation, renamed itself and eventually dissolved.
After that a earlier small splinter group decided that since the name wasn't being used any more, they would have it, and started operating as the CPGB (Provisional Central Committee). This is the group that publishes the Weekly Worker paper.
As the biggest remaining group, the CPB now often just calls itself the Communist Party.
There were other groups but I don't know if any are still active.