The UK Labour Party didn't really cease being of the left and away from nationalisation until 1983, which started the march to being "Tory Lite" of Blair's New Labour. [1]
Around 1980 the centrist people split away from the party to form the SDP (they would much later merge with the liberals to become the LibDems).
What killed the left was "the longest suicide note in history" - Michael Foot's 1983 Election Manifesto. 1983 was the early election that Thatcher used to cash in the Falklands dividend. The Tories were on course for a major loss, or at best scrape a hung parliament prior to the Falklands, after they got a doubled majority and the pattern of the rest of the decade was set. No Labour manifesto policies could have answered that. Yet between that and the SDP it started the journey to Blairism, and almost destruction of the party.
Brexit may end up doing similar to the Tory party - they've kicked many of their moderates. Depending what the December election brings, it could get ugly... Bring popcorn.
[1] OK, if you want to be pedantic, the IMF loan Healey got in 1974, and subsequent IMF supervision kicked them toward the centre -- temporarily. Everyone remembers it was Healey -- no one remembers the negotiations started the moment they got elected because the Tories left no public finances, and of course there was that minor oil crisis. :)
>The British Labor Party, whose leaders compete with their Con-servative counterparts in advancing national interests, is hard put to save even a modest program of partial nationalization. In West Germany, which has outlawed the Communist Party, the Social Democratic Party, having officially rejected its Marxist programs, is convincingly proving its respectability. This is the situation in the leading industrial countries of the West. In the East, the gradual reduction of direct political controls testifies to increas-ing reliance on the effectiveness of technological controls as instruments of domination. As for the strong Communist parties in France and Italy, they bear witness to the general trend of circumstances by adhering to a minimum program which shelves the revolutionary seizure of power and complies with the rules of the parliamentary game.