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Corbyn, who has been criticised for avoiding tough questioning by only appearing on the Today Programme once since becoming leader, agreed to answer questions from Wiggins, one of several people to guest edit the Today Programme over the Christmas period.
They started off the interview by comparing bikes. Corbyn showed off his aluminum Raleigh bike to Wiggins and joked about one of the most famous times he has been misrepresented in the media: an article in the Times newspaper that accused him of riding around on a "Chairman Mao-style bicycle." As Corbyn correctly pointed out to Wiggins, his bike is a modern lightweight machine, unlike the heavy "Flying Pigeon" bikes used in Communist China.
"I think whoever wrote it was a Chairman Mao bicycle should be sent away for reeducation," Corbyn joked while making a reference to China's "Re-education through labour" camps that force political dissidents to undertake years of hard manual labour.
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"I never really thought I would be appointed to any sort of position so my aspirations, in so far as I had any personal aspirations," Corbyn told Wiggins, before adding that he is "very ,very proud" to be leader.
The job can be tough, though.
"It is a huge amount of work and pressure but basically very enjoyable," Corbyn said. "I quite enjoy pressure. I don't worry about things particularly. I just get on with it," he added.
Corbyn also opened up to Wiggins on the importance of having a life outside of
Wiggins did manage to get in a couple of more serious questions, including asking Corbyn whether he really could envision a day when he ended up as Prime Minister. "Yes. Yes we could," he replied.