Two excellent examples, though I wouldn't say the party can be defined by its leaders so easily; least not by such a consensual leader like Attlee who is almost the opposite of a dominating "one-man-party" type
That's true, but the record of the Attlee government was something that even the
younger senior Labour figures were firmly associated with.
They did indeed try to paint Bevan as a dangerous extremist, but I don't think anyone who wasn't a retired colonel in reality - or in spirit - ever believed he was 'soft on communism' (by the end of the 40s he was pretty bluntly hostile towards the Soviet Union, and kept moving in that general direction throughout the rest of his life.* Though generally in a classic Left-of-the-Left way that was also deeply sceptical of the Americans), and, anyway, he was a popular figure: very unlikely that they picked up many votes that way. But, basically, 'communism' hardly featured in Conservative campaigns during the Cold War - this was not the case in the '20s and '30s.
Worth noting - very briefly - that there were always elements on the Labour hard Left who were less than hostile towards the Soviet Union, but they were generally kept as far away from the front bench as possible.
*He was involved, as were many other senior Labour figures, in the less than sober (but very sincere) heckling of Khrushchev during his visit to Britain in 1956.In Britain I think the Cold War was felt more in the '50s than the '70s, but
basically yes. Wilson might have been thought of as a Soviet spy by the more deranged elements in MI5, but he backed the Vietnam War (the Vietnam War!) - even if he was clever enough to not get British troops involved - despite hailing from the Labour Left.
Developments on the Left of the Left in the 70s and 80s are where things start to get deeply weird, yes.* But they were generally looked on with hostility by the leadership. It's notable that when Labour was attacked in the 80s for being extreme it wasn't really attacked - at least not often - in Cold War terms. 'Loony Left' rather than Reds Under The Bed or whatever.
*The weirdest part was that the CPGB basically ceased to be a Communist Party in anything other than its personal finances.The Australian case is an interesting one, yeah. Though I do always wonder to what extent 'Communism' was a code-issue for other things.