He insisted he did not intend to challenge Mr Corbyn for the leadership, saying “I don’t think there’s any vacancy right now” and that he was “confident” the Islington North MP would lead them into the 2020 election.
But he continued: “I think any politician who comes into this to want to try and change the world for the better, starting with their own patch and working outwards, I think they’re either in the wrong game or fibbing if they don’t say, 'if you had the opportunity to be in charge and put in place your vision for a better Britain would you take it?'.
“Yeah, of course, it would be an incredible honour and privilege to be able to do that.”
The 45-year-old MP only entered Parliament in 2010 but quickly won the respect of his colleagues and was promoted to shadow secretary of state for Wales by former leader, Ed Miliband, in 2012.
In pictures: Jeremy Corbyn reshuffle
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When asked about the reshuffle and Mr Corbyn’s record so far, Mr Smith refrained from criticising him.
He said: “Being sacked from any job is never a nice thing and I’m sure they’re both mightily cheesed off about it.
“But Jeremy won and is within his rights to have a reshuffle and we’ve just got to move on.”
He said that instead of focusing on internal disputes, Labour should turn its attention to challenging the “really rotten, right-wing ugly Tory government in place right now”.
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