As others have said preventing WW1 helps.
OTOH I'm not sure what the Liberals could have done to continue to persuade large sections of the working class to continue backing them as socialism spread through Europe and attracted more people.
Labour were growing quickly before the war although they had a small setback in the second 1910 election (possibly a shortage of funds after fighting one election earlier that year).
I think they would have continued to grow until they reached the point that they divided the anti Tory opposition (as the SDP/Libs did in the 1980s) to the point where the Liberals couldn't win power alone. Also the more Labour grows the more right wing Liberals would be frightened into joining the Tories.
Eventually some kind of Lib/Lab coalition government would have been elected. Then the left wing Liberals jump over to Labour.
I'm very skeptical of the view that the twentieth century experienced a universal explosion of working class consciousness and therefore a dramatic rise in support for socialist parties. Even if this class-based interpretation is assumed to be true, the British working-class was fragmented and relatively apolitical. Also, the Liberal party by 1914 had adapted well to an emerging focus on social issues, as Peter Clarke's classic
Lancashire and the New Liberalism showed. I don't think that the Labour party were growing that quickly before the war, most of the evidence used to support this view originates from local election results which were very variable and often totally unrepresentative of Labour's performance at a constituency level.
More importantly, the idea that British politics was dominated in the early twentieth century by "class consciousness" is flawed. There was no straightforward link between political activity and objective economic conditions or interests, as much of the "New political history" work has convincingly shown. Labour did not passively benefit from social change but made its own success, it was very fortunate to be in a position to take advantage of the Liberal schism and adapted well to the mass media in the 1920s to reach out to a wide range of social interests. I can't really see Labour breaking through without a significant political development such as the Asquith/Lloyd George spilt or a social upheaval such as the First World War. It's possible that Labour may still displace the Liberals, but I find it unlikely, at least in the short-term.