If you're a left wing/socialist person, there's not a lot of appeal in a sequence of governments that goes: Tories get in and reform to the right, Labour centrists get in and keep things the same, Tories get it and reform to the right, Labour centrists get in and keep things the same, ad infinitum.
During the 20th Century we had a Conservative PM for something like 60% of the time and Lloyd George, a Liberal, required Conservative support for 6 years.
I know by the end of the Century there had been a significant widening of inequality, but can you really say that the century was not a big shift for the left?
Universal Suffrage, Workers Rights, Pensions, Unemployment Benefit, the NHS, anti-discrimination measures, the minimum wage etc etc.
The British tend not to like big changes if they can help it. Evolution not revolution as it were. Marx laughed at the idea of Britain as a candidate for a communist revolution. So for most of the time the left win by nudging the Conservatives along gradually. The one overriding principle the Conservative Party have is staying in power, so if it a choice between keeping things as they are and losing power, or shifting slightly to the left to stay in power, then they will move, albeit reluctantly.
For the big shifts, the long overdue shifts, they don't come from the Tories usually. In and out of Europe might be the only ones. The big changes came from the Liberals 1906-1914 welfare reforms, with Asquith/Lloyd George's (and Churchill's), which in part was a response to the emerging Labour Party. Then we have Atlee's massive reforms - Health, Welfare, Housing, Nationalisation, Workers Rights, Education.
Thatcher obviously changed many things too, but even her attacks on the unions didn't impact things like H&S measures which by then were being enshrined in law.
Blair reset priorities again, with emphasis on increased spending on Education and the NHS, equality and introducing the minimum wage.