What these 'soft left' people don't understand is that Margaret Thatcher was both perceptive and correct when she stated, truthfully, that her greatest success was the 'creation' or 'emergence' of New Labour, because this meant the utter defeat of the left and the threat of socialism.
She knew what she was talking about. New Labour became just another version of the Tories, like the Liberals. So now we have three Tory parties. Three factions virtually indistinguishable from one another with no real significant ideological or political differences discernable, apart from rhetorical ones, which keeps the politically active and the media happy and employed.
That these obvious truths are ignored by vast swathes of the left, is understandable, but pathetic.