You probably know more about this than me, but heres how I see it...
He WAS democratically elected by grass roots members of his Party, that is beyond question. I think that what IS being questioned is the nature of that membership. There was large scale entrism by groups, including SWP, in line with Militant infiltration in the 80s. They grouped together, paid their 3 quid, and got their man elected. Now, they seem hell-bent on remaking the whole Party in his image, even if he will never be PM while his ar5e points south !
The likes of Dave Nellist and Derek Hatton tried it in the 80s