You don't need anything as dramatic as death squads or revolution...
You only need a few small changes right at the start of the period.
The Labour Party began life as the Labour Representation Committee in 1900. As in, a political committee that explored ways of representing labour [ie the Trades Union movement] in established politics.
Up until this point many Unions had backed the Liberals as the more 'worker friendly' party and the first two decades of the twentieth century saw a period of jumping ship on the left from Liberal to Labour.
That said, some established Trade Unionists remained skeptical about the LRC, particularly those who did not directly associate pro-worker politics with the socialism that coloured the early LRC. Important figures like John Burns and John Ward never abandoned the Liberals, though, remaining outside of Labour.
You would only need a little more skepticism and conservatism amongst the Trades Union to see the LRC, and the subsequent Labour Party, struggle to get off the ground. If significant Unions like the groups that later became the TGWU etc failed to see the LRC as a viable option, or were put off direct political engagement as a strategy, then you would essentially see the Labour Party never really go beyond a small-scale single-issue pressure group.
Changing this, however, requires you to make the Liberal Party more of a standard bearer for the trades union movement to stick with.
some ideas:
Lloyd George succeeds Campbell Bannerman not Asquith - as much as I love Asquith, he was much to middle-class for the Trades Union. Lloyd George, on the other hand, in the 1900s, was very much the darling of the radical movement.
Have the Liberal Party of the interwar period be seen as the destination for Radically inclined young ideologues. Some of the Labour generation of 1945 are going to stay in the Trades Union movement in this scenario [Bevin, Bevan, etc] but others are going to gravitate towards political movements [Atlee, Stafford Cripps, Morrison, etc]. This would give the radical wing of the Liberal Party a new edge in a period where many in British Politics were searching for new answers.
Prevent the economic orthodoxy of the 19th century Liberals spilling over into the new century - they need post 1900 to stop seeing Free Trade as the central pillar of their identity as the Trade Unions will never buy this and will start looking to throw their support elsewhere.
