**** The official name is the Communist Party, just as the Labour Party is its official name rather than the Labour Party of Britain. Also "Britain" is NOT a synonym for the "United Kingdom" but Great Britain is accurate as it excludes Northern Ireland where this party does not organise. (    ) 
 ***** As for disambiguation there are three Socialist Party articles on wikipedia but the ambiguity is dealt with at the top of each article Socialist Party (England and Wales) Socialist Party of Great Britain British Socialist Party. The same can be done with this Communist Party and the old CPGB. As has now been done Communist Party of Great Britain (disambiguation) (    )