Owen Smith has become the first shadow cabinet member to state his interest in standing for the Labour leadership. In an interview with the New Statesman, the shadow work and pensions secretary said it would be "an incredible honour and privilege" to do the job. Smith, the MP for Pontypridd since 2010, has been spoken of by colleagues as a possible "soft left" successor to Jeremy Corbyn.

Asked whether he would stand in the future, the former shadow Welsh secretary said: "I don’t think there’s any vacancy right now. But 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?' Yeh, of course, it would be an incredible honour and privilege to be able to do that."

Smith emphasised, however, that he expected Corbyn to lead Labour into the 2020 general election and offered a more unambiguous endorsement than some of his shadow cabinet colleagues. "Jeremy is going to lead us into the election, he’s the leader of the Labour Party ... He’s said very, very clearly that he wants to take us into the next election, he won a stonking great majority. Jeremy is going to be taking us into the election in 2020. End of." In a recent interview, Angela Eagle, the shadow business secretary, refused to say that Corbyn should remain leader until the election.

Elsewhere in the interview, Smith said that Labour should remain a "broad church" but did not criticise the sacking of former shadow culture secretary Michael Dugher and shadow Europe minister Pat McFadden. "I think that’s for the leader, to be quite honest, I really do. It’s not for me. He could sack me tomorrow and therefore that makes clear what my position is. I’m someone who serves in Jeremy Corbyn’s shadow cabinet, they were people who served on Jeremy Corbyn’s frontbench, I think they’re both talented politicians, very talented, I think they’ve got a lot to give to the Labour Party, I’m sure they will do in future, they’re also friends of mine.

"Being sacked from any job is never a nice thing and I’m sure they’re both mightily cheesed off about it. Jeremy won and is within his rights to have a reshuffle and we’ve just got to move on. I know those two individuals who are both very experienced, mature, serious politicians will pick themselves up and move on and do what they come into politics for which is to improve the lives of their constituents and their communities."

Smith announced that he would soon begin a review of social security policy for the party. Corbyn has pledged to abolish the household benefit cap but Smith said that the current limit of £20,000 (£23,000 in London) should be reformed, rather than scrapped. "We’re in favour of there being a measure that would guarantee that you couldn’t have unlimited benefits for one household, I think there has got to be some means of doing that," he said. He added: "It's becoming increasingly evident, in my view, that the current cap that we’ve got doesn’t work, doesn’t reflect what they originally said, isn’t getting people back into jobs, isn’t saving money and therefore we’ve got to be confident enough to say if this thing isn’t working why should we simply row in behind it?"