Steve: 600,000 people joined the party when Jeremy became leader.
Is there any evidence of that claim?
Nowhere that I can find ever shows the recent total membership in that range, let alone a sudden surge of that amount.
According to The House of Commons As of July 2019, Labour had 485,000 members,

I can see a prediction of total membership of that value in The New Statesman : Labour membership is on course to hit 600,000, a half-century peak, after a second successive day in which more than 100,000 people have applied to become party members. That does seem to imply that 600,000 may have been the membership 50 years ago though.

And according to The Guardian The membership level had fallen in 2019 from 518,659 at end of 2018 to a figure which remained above 500,000 as at August 2019