Somehow the news that Jeremy Corbyn enjoys eating cold baked beans out of a can comes as no surprise.

He comes across as a frugal socialist rather than the champagne kind, more interested in a good book than a good dinner.

What we don't know about Corbyn is whether he is going to destroy the Labour Party.

There's always been a tendency on the left to believe that the British public is ready to embrace proper left wing ideas, and the only thing stopping them is a steady diet of misinformation from the "right wing media" and treacherous Labour MPs who insist on tacking to the right – for example, by talking about limiting welfare payments.

Labour MPs themselves tend to have very different ideas about what the public wants.

They will point out they are the ones who actually knock on doors and hear what people are saying – and they know that British voters just don't hold the opinions that a portion of left-wing activists think they do, or think they should.

We may soon find out who's right.

It's still possible that Corbyn will lose the Labour leadership contest. But if he wins then we'll discover whether the British public really is crying out for socialism.

Having said that, Corbyn's supporters appear themselves to be divided. Some look at the packed meetings full of Corbyn supporters and the vocal backing he receives on Twitter and Facebook and conclude that he must be a vote-winner (although you would have assumed Ed Miliband was a shoo-in to be the next Prime Minister based on Twitter sentiment in the General Election).

Others say unashamedly that actually winning a General Election isn't the top priority, and they want Corbyn to win so he can shift the debate to the left, or because he will oppose (although not necessarily replace) the Conservative government.

It seems strange that some Labour supporters don't particularly want a Labour government. But perhaps that's because they don't think Labour achieved very much the last time they were in power.

This leadership election has exposed Labour's failure to defend its record, even to its own nominal supporters.

Former prime ministers such as Gordon Brown and Tony Blair, and former cabinet ministers including Alan Johnson and David Miliband, have urged the party to reject Corbyn, albeit without mentioning him by name in the case of Gordon Brown.

The response has been a wave of scorn for the previous Labour government and those involved in it.

Keeping the Conservatives out of power for 13 years, introducing the minimum wage, significantly increasing NHS funding, expanding anti-discrimination legislation, creating a new Sure Start service for parents, building new schools and hospitals, cutting pensioner poverty – these achievements don't seem to mean anything today.

Instead, "New Labour" politicians, and just about anyone refusing to back Corbyn, are castigated as Tories or Tory-lite by his more fervent supporters.

And in a way, who can blame them? Ed Miliband, who led the party from its traumatic 2010 General Election defeat to May this year, showed no desire to defend the record of the last Labour government.

And the shadow of Iraq hangs over Tony Blair, although it's not as if his party has made an effort to remind voters that his government also did other things.

Corbyn's opponents have descended into an unseemly struggle as they attempt to work out how to respond to his insurgency.

Yvette Cooper, the Shadow Health Secretary, has chosen to take him on directly – joining those who warn that Corbyn cannot win a General Election, and making him leader would be a disaster for the party and the country.

Andy Burnham, the Shadow Home Secretary, has prevaricated. Sometimes, he predicted armageddon if Corbyn won, but he's also attempted to appeal to Corbyn supporters, claiming: "There is a good deal of common ground between Jeremy and I on some of the big ideas he has brought to this race."

He also promised to include Corbyn in his "team" in some form, though it is unclear whether that means a shadow cabinet job or something else.

This has enraged Cooper's supporters, who say this sort of talk does nothing to dissuade people from simply voting for Corbyn.

In fact, the Cooper team responded by suggesting Burnham should simply pull out of the contest. A spokesman said: "If he isn't prepared to offer an alternative to Jeremy, he needs to step back and leave it to Yvette."

Of course, Burnham's supporters responded badly to that.

While neither Burnham nor Cooper have given up hope of winning the contest, the growing bile between their camps reflects the fact that they have half an eye on a future leadership ballot.

If Corbyn wins this time around – and it goes horribly wrong – Cooper's team wants to make it clear that she tried to prevent it.

And the Cooper camp wants to accuse Burnham of boosting Corbyn, through his "flip-flopping".

Some of Corbyn's supporters imagine that the media and "right wing" Labour MPs criticise Corbyn because they are scared of his socialist ideas.

Sadly for Labour, this is nonsense. This leadership contest really has become an utter disaster for the Labour Party.