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Well, he doesn't quite say that. He says he voted 'remain' and hasn't changed his mind, but as a second referendum is purely hypothetical, he doesn't actually say he would vote 'remain' in it. I don't think it's a 'game changer', he's just being honest and answering the question fairly casually, as it's not a big deal (and all those who pretend it is are probably just looking for the big political story of the day; that said, by the way she gave her answer, May certainly made it into a bigger issue for herself--it's a bit like the 'what's the naughtiest thing you've done?' question, which Corbyn adroitly deflected and May made a complete mess of). At the same time, he stresses that Labour respects the referendum result.
https://www.theguardian.com/politics/2017/oct/12/jeremy-corbyn-says-would-vote-remain-second-eu-referendum?CMP=twt_gu
Corbyn says he would vote remain in a second ref.
Game changer.