Was the British electorate "woke" in 1945, 1950, 1951 and 1955? In 1945, Winston Churchill lost a General Election by a landslide while the Second World War was still being fought. In 1950, he lost again. And in 1951, he lost the popular vote. But in 1955, after his party's presumably "woke" MPs had removed him, then that party won with what remains the largest share of the vote since the War.
Those are the facts. That is history. Anything else would be "rewriting history", and would be impossible to teach, since any self-respecting teenager with an interest in the subject would rightly laugh at it.
Back when the New Right was still the New Right, then it did not like Churchill. Eminent Churchillians is largely a critique of his Indian Summer Premiership of 1951 to 1955, for tolerating Coloured immigration and for "appeasing" the trade unions. Perhaps he was the "woke" one after all? Then again, perhaps not.