CPB Communist party of Britain, probably the largest socialist party in the country.
CPB-ML Communist party of Britain Marxist-Leninist, As the name suggests, an explicitly ML, anti revisionism, party.
CPGB-ML Communist party of Great Britain Marxist-Leninist, Another explicitly ML party.
WPB Worker's Party of Britain, George Galloway's party, has links to the CPGB-ML.
NCP New Communist Party of Britain, despite the name, one of the oldest communist parties in Britain.
RCPB-ML Revolutionary Communist Party of Britain, Hoxhaists I think.
Stalin Society, Their name pretty much says what they do.
That's all the orgs I can think of right now, I'm not very familiar with some of them.