Two senior shadow ministers have hinted they will resign if Jeremy Corbyn succeeds in dropping Labour’s support for the Trident nuclear weapons programme, highlighting tensions at the highest level of the parliamentary party.

Owen Smith, the shadow work and pensions secretary, and Lord Falconer of Thoroton, the shadow justice secretary, both renewed their support for Trident on Sunday. Smith said it would be difficult for him to remain in the shadow cabinet if the party supported a policy of unilateral nuclear disarmament. Lucy Powell, the shadow education secretary, added that she did not expect the policy to change.

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The shadow ministers were asked about Trident after the Independent on Sunday reported that the leadership was seeking to ease the process of changing party policy by strengthening the role of the national executive committee at the expense of the shadow cabinet. This would allow the policy to be changed before an expected Commons vote in the spring on the renewal of Trident.

Asked on Pienaar’s Politics on BBC Radio 5 Live if a change in policy would lead to his resignation, Smith said: “Well that would be difficult for me but I think the key thing that I would do is stick in, in the run-up to that decision, and make the case.

“We have got to have, I think, a very adult argument in the Labour party about this – not in public I hope, not in the way in which we have occasionally argued publicly recently. But it is an enormously serious, technical, strategic question for Britain as to what the nature of our nuclear weapons are and whether we have a nuclear deterrent. My view is that unfortunately we do need one.”

Falconer said in response to a similar question on The Andrew Marr Show on BBC1: “Let’s see what happens in relation to that but I am clear that I support Trident remaining.” The shadow justice secretary also rebuked Corbyn for sacking the “absolutely exceptional” Pat McFadden from the shadow cabinet.

In a sign of continuing frontbench divisions after the reshuffle, Falconer said he wholeheartedly agreed with McFadden’s warning last year about drawing a link between terrorist attacks and western military intervention. McFadden was told that his remarks, in which he spoke of the dangers of infantilising terrorists, had been seen as disloyal to Corbyn, who spoke after the Paris attacks of the legacy of 14 years of western military intervention in Iraq and Afghanistan.

Falconer said: “Pat McFadden said there is no excuse, you can’t justify what terrorists have done because of any allegation about what the west’s policy is. I obviously agree with that proposition so I regret that Pat has gone. The decision as to who is in and who is out of the shadow frontbench team is entirely a matter for the leader.

“My own view about Pat McFadden is that he was an absolutely excellent [shadow] Europe minister. I have known Pat over a very long period of time and he is an absolutely exceptional public servant. I certainly would not have fired him.”

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In an interview with the Sunday Times, McFadden defended his views on the motivation of terrorists and the link with UK foreign policy. He said: “This view of the world seems to separate the world into adults and children, and the adults are the west the others – the children – are anti-west. That’s not the way the world works.

“If we see acts of terrorism as a kneejerk response to what we’re doing, then we do run the danger of not placing responsibility where it firmly lies. I do believe that no one forces anyone to kill people in a theatre in Paris or blow up the London Underground,” he added.

McFadden also condemned Corbyn for not intervening when his shadow chancellor, John McDonnell, branded those sacked in the reshuffle as “hard right”.

“It’s an attempt to demonise and delegitimise people and stop other voices being heard,” he said. “The use of rhetoric like that is not what Jeremy promised when he took over. He said he would practise a kinder politics without personal attacks.”

Falconer, who once shared a flat with Tony Blair and was one of his closest allies in office, is one of a number of former ministers who are not natural Corbyn supporters who sit in the shadow cabinet. In his interview he said that he believed Corbyn could be prime minister. The leadership welcomed his remarks on Corbyn.

