You can see how the election results roughly overlap with trends in membership.
The membership peaked at 56,000 in the 1940s, the party gained two MPs in 1945.* If you check the publications from around that time it’s clear that the party maintained an extensive network of local offices and bookshops, it was firmly embedded in the labour movement and had representatives in city councils across the country. I can only imagine what that period must have been like.
* There’s always some nerd who pipes up to point out well actually, what about the (five?) communists who were elected ‘as Labour MPs’, or Baron Wogan Phillips who was a communist in the House of Lords, or Cecil Malone who was elected as a Liberal MP but joined the Communist Party in its early days. Don’t worry, they haven’t been forgotten.