The WSL was founded in 1975 with a leadership grouped around Thornett, Tony Richardson and John Lister.
It published the weekly paper Socialist Press and a number of issues of a theoretical journal Trotskyism Today.
The first factional struggles were the result of the development of a small group of supporters of the American Spartacist League.
The result was that they recruited a number of WSL members to their views and these formed the Leninist Faction in 1977.
In 1978 the United Secretariat of the Fourth International invited the WSL to submit material to the USec's 1979 Eleventh World Congress.
This also had a reaction in the Labour Party which swung to the left and began to attract the attention of Trotskyist groups including the WSL.
The I-CL disagreed with this view and took a dual defeatist position on the war on the grounds that Argentina was not a semi-colony of imperialism, and also called for self determination for the Falkland Islanders.
Others sympathised with the international tendency around the Workers' Party (Argentina), the Latin American Tendencia Cuarta Internacional (TCI).
The WSL then walked out after a resolution calling on Alan Thornett to fight Sean Matgamna's "revisionism".
Thornett's supporters stopped paying subscriptions to the group and called several special conferences.