Accurate or not, it would not surprise me if class based voting in Britain is declining. It certainly has in the US. I mean, after all, both Labor and the Dems focus most of their efforts on appealing to the middle class, no?
"Middle class" has a different meaning in the US and UK. In the US, pretty much everybody who isn't Bill Gates or homeless is considered "middle class."
The British Labour Party, unlike the socialist parties of the continent, was never Marxist. But I guess to you Fabianism and Marxism are indistinguishable.