National Executive Committee

The Labour Party is run by its National Executive Committee, one of whom, Christine Shawcroft of the Hard Left was kicked out for backing Lutfur Rahman, a greasy Pakistani crook when he was opposing Labour. She has been readmitted since Comrade Corbyn took office in 2015. The NEC is controlled by Ken Livingstone and his peculiar friends, who are also part of the Hard Left.  See e.g. Private Eye 1403/13 on the point.
PS The current [ 2015 ] propaganda chief is Seumas Milne, a Stalinist public school man.

National Executive Committee ex Wiki
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The National Executive Committee (NEC) is the chief administrative body of the Labour Party. Its composition has changed over the years, and includes representatives of affiliated trade unions, the Parliamentary Labour Party and European Parliamentary Labour Party, constituency Labour parties, and socialist societies, as well as ex officio members such as the Party Leader and Deputy Leader and several of their appointees.

During the 1980s, the NEC had a major role in policy-making and was often at the heart of disputes over party policy. In the Tony Blair era, the committee's role declined and its membership was reformed, but it remains the administrative authority of the party. Its former policy development function is now largely carried out by the National Policy Forum. One of its committees has disciplinary powers including the ability to expel members of the party who have brought it into disrepute or to readmit previously expelled members.
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The Wiki tells some of the truth some of the time. What do they miss out? It depends on the agenda.