This does not mean that Pollitt's government would be all sunshine and roses, but if he were to get the Scots back on board and make peace with some of the other rebel organisations he would have been forced to maintain something closer to old Britain than to the Soviet Union. (Though, that's IF. It'd make for an interesting sight to see what happens if he didn't)
Given the track record of communists in OTL such as how during the Spanish Civil War, the Stalinists were seemingly more interested in purging their fellow leftist Republicans that do not answer to Moscow using death squads staffed by NKVD advisors of instead of actually fighting the Nationalist, or the way in which the Bolsheviks during the Russian Civil War liquidated Makhno and his Black Army anarchists by firing squad while they were in the middle of the conference with Red Army commanders and the Bolshevik-Makhnovist treaty was still active....
Frankly, I see the idea of the leadership of a Leninist revolutionary/resistance organization willingly playing nice and even compromising with any other resistance movement, even fellow leftists, that does not fit into the exact same ideological orthodox as themselves
(Let alone resistance movement led by 'reactionaries' such as HMMLR), while they are in a dominate position of strength over the others, sort of like one of those 'Notzi' TLs where Hitler and the Nazis go OOC by actually acting in a sensible and reasonable manner by not being genocidal racist maniacs.
This is my personal political bias speaking here: But I would say that Red Terror and betrayal against fellow revolutionaries that disagree with them the moment the latter have outlived their usefulness against their common enemy
(And often times they couldn't even keep it in their pants for that long, as both the examples that I have cited above took place before the Nationalists/White Army were even defeated) is a fundamental and unalterable feature of communism, something deeply hardwired into the ideology: It is exactly what one would and should expect from a group that believe the ideology that they cling to is the final evolutionary leap of humanity's historical development. With such absolute truth in their hands, why would they NOT get rid of all the reactionaries, revisionist, and class enemies that opposes what they see as the inevitable historical progress the moment they are in a position to do so?
If the Left resistance had won the First London Uprising, assuming that Hitler don't just throw a temper tantrum and order a nuke to be dropped on London (The Nazi's pre start date plot armor is still in effect here), they would not have given up an inch of ground to the other resistance organizations or even the more moderate members within their ranks. The people of England will have a communist dictatorships imposed upon them at the point of a gun, being move from getting trampled under the Nazi jackboot to the Communist jackboot. By the mod's start date, would things be better for the majority of the population under the communists compared to the Collabs, especially with OFN aid rushing into the country to to give the Americans a foothold on Europe once again by propping up an anti-Nazi regime that have nowhere else to turn to? Of course. But compared to the better HMMLR or even collab outcomes that England can get in OTL TNO, I would say that things would most certainly be worst.
And in the end, after their power was broken by Battle of Cable Street, even the surviving communist hardliners such as Birch were forced to work together with moderates such as Wilson and even 'reactionaries' such as Auchinleck... But only because they were forced to do so.... For now.