Jeremy Corbyn would instruct the UK’s defence chiefs never to use the Trident nuclear weapons system if he became prime minister in 2020, the new Labour leader has confirmed.

Corbyn made his statement in an interview with BBC Radio 4’s Today programme on Wednesday in which he said he had a mandate from his election to oppose the replacement of Trident and the use of nuclear weapons.

It is likely Corbyn will come under pressure from those who will question why he would not even fire back at nuclear weapons being trained on the UK. He said: “I am opposed to the use of nuclear weapons. I am opposed to the holding of nuclear weapons. I want to see a nuclear-free world. I believe it is possible.”

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Asked if he would use nuclear weapons, he said: “No.” His remarks underscore his longstanding opposition to nuclear weapons, but put into perspective the long-term nature of the debate about whether the Commons should vote next year to replace Trident, a process that is not due to be completed until 2028.

Corbyn said: “There are five declared nuclear weapon states in the world. There are three others that have nuclear weapons. That is eight countries out of 192; one hundred and eighty-seven countries do not feel the need to have nuclear weapons to protect their security. Why should those five need them to protect their security? We are not in the cold war any more.

“I don’t think we should be spending £100bn on renewing Trident. That is a quarter of our defence budget. There are many in the military that do not want Trident renewed because they see it as an obsolete thing thing they don’t need. They would much rather see it spent on conventional weapons.”

The Labour leader said he recognised that other shadow cabinet members held opposing views on the issue, saying: “I am very well aware of the views of a large number of party members and supporters who were quite prepared to vote for me knowing full well my views on nuclear weapons. It would be dishonest of me to say anything less than my honest view on it.”

In other broadcast interviews, Corbyn did not rule out giving MPs a free vote on the possible air bombing of Syria, stressing that such a vote was hypothetical.

His close ally John McDonnell said in a Guardian fringe meeting on Tuesday night that efforts to reach consensus in the party were continuing but MPs might end up having to “agree that we can’t agree”.

McDonnell said: “When you are sending people to potential loss of life, I think it is a conscience decision. It is a moral decision. On Syria, my view is it should be a free vote on the basis of conscience.”

Corbyn also defended his decision not to mention the deficit during his first conference speech as leader, saying he did not believe there was a way to cut Britain to prosperity.

He argued instead that it was better to grow to prosperity. He said Labour had not been clear enough at the last election and suggested that the 36% of people who did not vote were not sufficiently persuaded by Labour’s offer or the clarity with which it opposed the deficit.

He refused to endorse remarks by the shadow home secretary, Andy Burnham, that Labour had not faced up to the unpopularity of the free movement of workers inside the European Union and this was one cause of the popularity of Ukip.

He said instead that services needed to be improved in areas of high immigration. “People who have migrated to this country over many years have made an enormous contribution to our society, helped our economic growth, helped our health service and helped our social services, so I don’t necessarily look on immigration as a problem. It is often a very great opportunity.”

Corbyn said it was better to look at the net figures for immigration, rather than the growth figures, and said the inclusion of student numbers gave a misleading figure.

Asked about the presentational aspects of his speech, he said he thought he had looked smart, and denied that he had borrowed large philosophical chunks from extracts sent to him by Richard Heller, a former adviser to Denis Healey, that had been rejected by other party leaders.

Corbyn said: “We were sent some information and ideas by a number of people in preparing this speech.”

He explained that the speech was more than 5,000 words long and 350 words were provided by a friend. “I like the way he put them forward. I like the words he used so I used them in my speech. What’s so bad about that?

“I quoted poets, I quoted Ben Okri, I quoted Maya Angelou. I referred to the works of Keir Hardie. I tried to make a speech about policies and philosophy and a message about the way in which politics should be conducted in this country. Not everyone will like the speech: you cannot please all the people all the time.”