Andy Burnham's campaign managers, John Lehal and Michael Dugher, the MP for Barnsley, have written to Labour's general secretary warning against "potential Tory infiltration on a large scale" of the Labour leadership election. They believe that the continuing purges show that there is an unresolved problem with supporters of opposing parties joining to cause havoc in the Labour leadership election. Are they right?

For context, some important numbers: there are 120,100 registered supporters - people who have paid £3 to have a vote in the Labour leadership election. The full electorate - which includes £3 supporters, trade unionists, and full due-paying members - is close to 600,000. Labour have rejected the applications of 3,000 people - party staffers vary on how many will ultimately be kicked out, with estimates ranging from 4,000 to 9,000 in total.

The two biggest parties that might join the Labour party to "wreak havoc" are the Conservatives and the Greens. There are close to 40,000 members of the Green Party - and around 140,000 members of the Conservative party. What about the parties of the far left? Michael Crick, who knows more about entryism than some entryists, puts the membership of the Militant Tendency at its 1980s peak at 8,000. It is now significantly lower.

Bluntly there simply aren't enough members of the Conservatives, Greens, Communists of various types to account for the surge in membership. Remember, too, that is overwhelmingly established members who have turned up to constitutency meetings to nominate Corbyn. Yes, there are some people who have joined to hurt the Labour party - and others who have flouted the rules of the contest unwittingly. Not all of those voters will be screened out by the party - and some people who deserve a vote won't get one. But the overwhelming majority of people supporting Corbyn have joined because they are inspired by his message, his policies and his campaign - and the margin of his victory will be sufficiently large than any grumbles about unfair entryism or supposed purges will frankly look a little churlish.