Labour MPs are eyeing up Hilary Benn as their next leader – after a torrid week for Jeremy Corbyn.

Backbenchers have been seriously impressed by the shadow foreign secretary in recent weeks, particularly his response to the Paris terror attacks.

At a meeting of the parliamentary Labour party on Monday evening, MPs loudly applauded Benn for his comments on ISIS and potential airstrikes in Syria. The warm reception was in stark contrast to the frosty silence that greeted Corbyn's remarks.

One senior Labour MP, who wished to stay anonymous, told BuzzFeed News they had since put money on Benn at 25/1 to become the next leader.

Benn, who has been MP for Leeds Central for 16 years, is viewed as the "unity candidate" who can bring together the pro- and anti-Corbyn wings of the party. The son of Tony Benn, the late former cabinet minister and left-wing campaigner, he has served on the front bench under Tony Blair, Gordon Brown, and Ed Miliband.

Labour MP John Mann laid bare on Wednesday how attentions were turning toward Benn. Asked whether he had faith in Corbyn in the wake of the terror attacks, Mann told BBC2's Daily Politics: "I have total faith and confidence, as does everyone in the parliamentary Labour party, in Hilary Benn.

"Everyone, including Jeremy, is having to tow in behind Hilary, who's giving the lead, and as long as Hilary continues to give the lead in this way we'll all be very happy because we're in the right place."

Many Labour MPs fear the party is heading for a crushing defeat under Corbyn at the next general election in 2020, and believe a new leader is the only solution. One MP told us: "We're in a car driving at top speed towards a cliff and the brakes aren't working."

But they also recognise there is little chance of Corbyn being immediately replaced because he won the leadership contest with a staggering 60% of the vote. One MP described Benn as a "rising star" but added: "There's no vacancy."

Next May's elections – for devolved bodies in Scotland, Wales, and Northern Ireland, the London mayoralty, and councils in England – will be a key test for Corbyn. A new leadership contest would be triggered if 20% of the parliamentary Labour party – 46 MPs – informed the party's National Executive Committee they supported a rival candidate.

Backbenchers were furious with Corbyn's initial response to the terror attacks in Paris which killed 129 people on Friday. He dodged questions from MPs on Monday about whether ISIS terrorists should be shot dead on British streets if innocent lives were at stake.

As the pressure grew, he was forced to release a statement on Tuesday clarifying that he supported "the use of whatever proportionate and strictly necessary force is required to save life in response to attacks of the kind we saw in Paris".

Corbyn also suffered a grilling from MPs over his apparent refusal to grant them a free vote over RAF airstrikes against ISIS in Syria. One shadow minister told the Daily Mirror: "He got roasted, he's a fucking disgrace."

And he refused to condemn the Stop the War Coalition, which he used to chair, for claiming at the weekend that Paris had "reaped the whirlwind of Western support for extremist violence in the Middle East".

Meanwhile there was fresh anger on Wednesday when it emerged Corbyn had appointed his close ally Ken Livingstone as co-chair of the party's defence review. Within hours, Livingstone had to apologise to frontbencher Kevan Jones for calling him "disturbed".

A spokesperson for Benn declined to comment.