Why did the U.K. roll back on its leftism?
And how did Thatcher succeed so much on the first place?
A combination of factors, like I said, from the mid 50s to the early 70s Britain enjoyed relative peace and prosperity, and for the most part governments that were both Conservative and Labour respected the welfare state and nationalized industries created by the 1945-1951 Labour government.
As with all the other Western economies, Britain experienced a particularly hard economic slump in the 1970s, and the decade was pretty much marked by industrial strife and the relations between the labor unions and the governments. In the winter of 1978-1979 a large number of labor unions went on strike in what's known as the Winter of Discontent. This made Jim Callaghan's Labour government extremely unpopular and led to a vote of no confidence and an election held in the spring of 1979, which Thatcher won.
Thatcher was so successful because of infighting between the Labour left and right in the early 80s, which debilitated the opposition from posing a major threat and led to the Conservatives election victory in 1983, and the North Sea oil, which turned around the economy and led to their second victory in 1987, and she used the cover of a strong economy to privatize much of the public sector, like utilities, industry and transportation. She had pretty much fundamentally changed Britain's economy from an industrial one to a service one, with a strong financial sector.
With this the opposition had to change as well, Labour largely gave up socialism and pursued more moderate, center left, social democracy after 1983.