Britain's parliament will vote this month on renewing the Trident nuclear weapons programme, Prime Minister David Cameron said Saturday as he sought to reassure NATO allies alarmed by Brexit.

Cameron's announcement at a NATO summit in Warsaw comes as the alliance grapples with the implications for its unity after key member Britain shocked the world by voting to leave the European Union.

Conservative leader Cameron is pushing through the vote on the �20 billion (23 billion euro, $25 billion) plan to maintain the submarine-based system before he steps down in September in the wake of the EU result.

"Today I can announce that we will hold a parliamentary vote on the 18th of July to confirm (lawmakers') support for the renewal of a full fleet of four nuclear submarines capable of providing around-the-clock cover," Cameron told a press conference at what will be his final NATO summit after six years in power.

"The nuclear deterrent remains essential in my view not just to Britain's security but as our allies acknowledge here today to the overall security of the NATO alliance," he said.

Britain is one of only three nuclear-armed NATO nations along with the United States and France, and holds a permanent seat on the UN Security Council.

But the EU referendum result has raised questions about its commitment to NATO, especially at a time when the US-led alliance is trying to remain unified in the face of an increasingly assertive Russia.

- 'Ultimate deterrent' -

Cameron however insisted that his country, which has what he said was the second biggest military budget in NATO, would remain a key member.

"This summit has underlined that while Britain may be leaving the European Union, we are not turning our backs on the world," he added.

"We are a country that is willing to deploy its troops... and we are a country with the ultimate deterrent," he said.

Cameron is likely to win the Trident vote as his party widely backs it.

The leader of the main opposition Labour party Jeremy Corbyn has opposed the upgrade but a significant part of his increasingly rebellious MPs are also likely to support it.

The future of Britain's nuclear deterrent is however in question as the submarines are based in Scotland, where the government is considering a second independence referendum following the Brexit vote.

Asked why he was pushing through the vote before handing over to his as-yet-undecided successor, Cameron said it was a pledge in his party's 2015 election manifesto "and we need to get on with that."

"I don't think it needs to be caught up in the leadership contest (of the Conservative party) and we will be doing it on the 18th of July," he said.

"It makes sense to hold this vote now, for it to go ahead so our military planners can get on the investment that is needed."