Labour leadership candidate Andy Burnham has said he would resign from the shadow cabinet if he was asked to oppose the renewal of the Trident nuclear deterrent.

His comment sets the scene for a potential early split in the party if the race to succeed Ed Miliband is won by frontrunner Jeremy Corbyn, who wants to scrap Trident.

In a speech in London committing himself to an "internationalist" stance, Mr Burnham also warned it was a "profound mistake" for Mr Corbyn to create doubt over Britain's future membership of the EU and Nato, and warned David Cameron not to try to "bounce" Labour into supporting military action in Syria.

He raised the prospect that he would hike taxes to increase spending on the armed forces following the Strategic Defence and Security Review, telling an audience of defence experts at the Royal United Services Institute: "The first job is not to save money, it is to keep this country safe."

Mr Burnham committed himself to maintaining the continuous at-sea nuclear deterrent at the current level, warning that cutting the number of submarines would provide only "part-time" cover which would "defeat the object of the exercise".

But he said Britain should aim to ensure that the planned £25 billion Trident update is "the last time we renew our nuclear deterrent" by re-energising moves towards multilateral nuclear disarmament. If elected prime minister, he would put disarmament on the agenda when Britain next hosts the G7 group of major powers early in the next decade, he said.

Asked whether he would quit a shadow cabinet led by Mr Corbyn if he was told to vote against Trident renewal in the Commons, Mr Burnham said: "The answer is yes. I couldn't support that position. It is the wrong position for Britain to take, so I wouldn't be able to go out publicly to defend it."

He added: "I believe it would be difficult to serve in a shadow cabinet or cabinet that had taken a different decision.

"Jeremy Corbyn has made a commitment to saying he will let the party come to a view on these issues and I think that is a helpful statement, but in my view Labour shouldn't be allowing any room for prevarication or equivocation on issues of such huge national importance."

Mr Burnham said that, as party leader, he would be willing to "look carefully" at extending Britain's air strikes against the Islamic State terror group into Syria - but only if the Government sets out "clear and definable" objectives and explains how they could succeed in the absence of "clear and sufficient capacity on the ground from a viable and united opposition".

Ministers must prove the legality of any proposed action "beyond question" and have a "credible" post-conflict plan, he said. He warned that "tokenistic" air strikes could have unpredictable consequences on the ground, potentially allowing "extremist forces to fill the void".

"Britain's involvement - if there is to be any - needs to be very carefully judged," said Mr Burnham. "The suggestion earlier in the summer that Parliament might have been recalled for a snap vote, or indeed that the vote might come the week after next or next week, I think is disrespectful to Parliament, to the opposition, but crucially to the public."

He added: "The Government needs to set out its case and we haven't seen that yet. We haven't seen a proposition. We haven't seen a plan for the ground forces and how you secure the areas affected afterwards. Until they do present such a case, there can be no support provided.

"The thought that we might be bounced into this decision is utterly wrong. I want to send a very clear message to the Prime Minister that if he is thinking of doing that, then he should think again."