Though it became common parlance on the communist street in the 1970s the term "Straight Left" goes further back in labour movement history. At the time I was told that Micholson chose the title of his fortnightly magazine as a tribute to D N Pritt, the post-war left Labour Hammersmith MP, whose constituency newsletter was called "Straight Left".
Perhaps other "formers" can shed more light on this. What is for sure is that it was a Labour slogan in 1945 as this poster makes clear

https://wdc.contentdm.oclc.org/digital/collection/tav/id/3195/

pip,pip,


H A R Philby
(Col.ret'd)