Stephen Kinnock, the ambitious Labour backbencher who has taken a prominent role in the campaign to save the Port Talbot steelworks, has said the shadow business secretary, Angela Eagle, would make a great Labour leader.

In an interview with the House, a magazine published for MPs and their staff at the House of Commons, Kinnock, the MP for Aberavon, warns that Labour must take “remedial action” if May’s local election results don’t “go the right way” – and tips Eagle as a potential successor to the current leader, Jeremy Corbyn.

“As a party, from top to bottom, from the leadership right through to our grassroots, we have to be judged by our results and, you know, if results are not going the right way you have to examine why that is and take remedial action on it because that’s what we’re elected to do,” he said.

“Success breeds success and failure breeds failure, so there’s absolutely no doubt that if we win big and do really well moving into 5 May and 23 June, then there’s no doubt your leadership is strengthened, your party is strengthened, there’s wind in our sails and you move forward from there. But if the results aren’t going the right way then clearly that’s a different situation altogether.”

Eagle – who delighted backbenchers with a punchy performance when she stood in for Corbyn at prime minister’s questions in December – is seen by some in the party as a dark-horse candidate if Corbyn were to face a challenge.

Kinnock said he had been impressed by her while they worked on pushing the government to provide more aid to the ailing British steel sector. “‘Impressive’ is absolutely the right word,” he said. “I see her as being somebody that’s going to be absolutely critical for the future of the Labour party.

“I think too many years have gone by where we haven’t had a woman leader. One thing I would say is that I think it would be fantastic and Angela would be a very, very strong candidate for that. You would have to ask her yourself in terms of what her plans and ambitions are but I am absolutely of the view that she has the capability to do the job.”

The son of former Labour leader Neil, Kinnock added that he would like to see his frontbench colleagues take a more “forensic” approach to holding the government to account.

“I think it’s important that we have a forensic approach in the chamber. Maybe I’m just a bit of a traditionalist on these things, but I like an approach whereby we interrogate the government over the despatch box, pick their arguments to pieces, not in a shouty or shrill way, but in a way which actually exposes the weaknesses at the heart of their arguments. I think we could be doing a bit more of that.”

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There is mounting speculation among Labour MPs that a poor showing in May’s local elections could prompt a leadership challenge, to be held once June’s EU referendum is over – but those sceptical about Corbyn’s leadership have so far failed to unite around a single candidate.

Senior party figures are far from united about what would mark “success” on 5 May. Corbyn’s election campaign co-ordinator, Jon Trickett, has pointed out that 2012, the last time these council seats were contested, was a high water mark for the party which is unlikely to be repeated; others, including Alison McGovern, chair of Progress, have said losing even a single council would be a “betrayal”.