If you look at those Communist parties in the West that have been most electorally successful in the second half of the twentieth century, you'll find that they, them being the Japanese and the Italian, were notable in that they were very early on able to establish themselves as independent of Moscow and Beijing.
My guess is as to why this helped is actually not entirely due to the fact that close allegiance to whatever the party line in the Soviet Union happened to be would inevitably give off airs of them being fifth columnists (though this certainly didn't help), and that their commitment to now broadly established democratic institutions was paper-thin if even that (though this certainly didn't help either), but rather that it made such a Communist Party appear... not particularly serious.
Made them appear more like they were LARPing with their Central Committees and Politburos and General Secretariats than that they seriously cared about improving conditions in the countries in which they were operating.
Consequently, even with a change in the electoral system, you are likely going to need more than that for the CPGB to approach anything resembling electoral success. And more than that may very well be as much as you having to make the CPGB adopt policies, strategies, priorities, and public relations that would, for all intents and purposes, make it a completely different party from what the CPGB was.