I agree with a lot of your points about pragmatism but there absolutely is factionalism on the left in the UK, unless (as it looks like you are doing) you say some of them are not actually leftist and therefore the remaining group is small enough that it’s not arguing with itself.
The right are also split but in normal times they are better at keeping the worst of it behind closed doors and rallying around the leader when the dust settles. Lack of message discipline is what kills the left at the ballot box. New Labour were good at it and they won; Starmer is trying to do the same - sensible tactic in my opinion.