London(CNN) British Prime Minister David Cameron has outlined his "big, bold, patriotic case" for the UK to stay in the European Union, saying that the country would be weaker and less-equipped to combat terrorism if it voted to leave.
In a speech Monday at the British Museum in London, Cameron argued that Britain's strength and security was inextricably linked to events in Europe -- and its ability to wield influence there.
"Britain has always been a European power, and we always will be," he said.
"Isolationism has never served this country well. Whenever we turn our back on Europe, sooner or later we come to regret it. We've always had to go back in and always at a much higher cost."
Cameron is campaigning for the public to vote to remain in the EU in a referendum on the issue June 23.
"This is a decision also about our place in the world, about how we keep our country safe, how Britain can get things done in Europe and across the world and not just accept a world dictated by others," he said.
Cameron spoke hours before Boris Johnson, the colorful Conservative member of Parliament and former London mayor, delivered an important speech in London outlining his case for why Britons should vote for a "Brexit," or British exit from the EU.
Backers of the Vote Leave campaign have focused on immigration in recent weeks, with senior government figures arguing that migrants from the EU are overloading crucial public services.
But Johnson, one of Britain's most popular politicians, took a different tack, making what he called the "liberal cosmopolitan case to Vote Leave."
He said he spoke for "people who love Europe and who feel at home on the continent, but whose attitudes towards the project of European Union have been hardening over time," frustrated by what he called its "anti-democratic absurdities."
He said the EU had "changed out of all recognition," that it eroded British democracy and was responsible for unnecessary regulation that stifled Britain.
"To keep insisting that the EU is about economics is like saying the Italian Mafia is interested in olive oil and real estate."
Johnson said that leaving the EU was not the same thing as leaving Europe.
"Of all the arguments they make, this is the one that infuriates me the most. I am a child of Europe. I am a liberal cosmopolitan and my family is a genetic U.N. peacekeeping force," he said, referring to his diverse ancestry.
"I find it offensive, insulting, irrelevant and positively cretinous to be told -- sometimes by people who can barely speak a foreign language -- that I belong to a group of small-minded xenophobes. Because the truth is it is Brexit that is now the great project of European liberalism, and I am afraid that it is the European Union -- for all the high ideals with which it began, that now represents the ancien regime."
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In his speech, Cameron argued that "the dangerous international situation facing Britain today means that the closest possible cooperation with our European neighbors isn't an optional extra -- it's essential."
"We need to stand united. Now is a time for strength in numbers," he said.
The threat posed by ISIS and international criminal groups meant "that we simply have to develop much closer means of security cooperation between countries within Europe," he argued.
EU membership, he argued, "amplifies our power."
"It helps us achieve the things we want, whether it's fighting Ebola in Africa, tackling climate change, taking on the people smugglers."
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Cameron invoked military victories in the 1805 Battle of Trafalgar and two world wars in underlining the role Britain played in Europe's history.
"The moments of which we're rightly most proud in our national story include pivotal moments in European history," he said.
"Our history teaches us the stronger we are in our neighborhood, the stronger we are in the world."
But he said British wartime leader Winston Churchill had never sought to have to stand alone against Nazi Germany's air force in the 1940 Battle of Britain. And after the war, he had actively lobbied for European nations to come together and build institutions that formed the basis of the EU so that future catastrophic conflicts could be averted.
"Can we be so sure that peace and stability on our continent are assured beyond any shadow of doubt? Is that a risk worth taking? I would never be so rash as to make that assumption," he said, referring to the massacre in Srebrenica that saw genocide return to Europe in 1995.
He said that leaving the EU would be "genuinely a leap in the dark" and that campaigners for a Brexit had failed to answer what access Britain would have to international markets if it left the single European market.
"They seem unable to set out a clear and comprehensive plan for our future outside the EU," he said.
"Some admit there would be a severe economic shock but assert nonchalantly that it would be a price worth paying. Others are in denial that they would be a shock at all."
The Treasury has calculated that the cost to every household in Britain would be as high as £4,300 (about $6,200) by 2030 if it country voted to leave, he said.
Membership in the EU was "one of the reasons why our economy is doing so well, why we have created almost 2.4 million jobs over the last six years," he said.
Arthur Burns, professor of modern British history at King's College London, said that the reading of British history presented in Cameron's speech -- in which he said Britain had always "come to regret" the times it had turned its back on Europe -- was "reasonably accurate."
But it was not clear what Cameron was referring to when he spoke of periods of isolationism that Britain had paid the price for later.
He said that Cameron was most likely invoking the 1930s, when "Britain tried not to get overly involved in continental struggles during the policy of appeasement, and then had to reverse that fairly rapidly in terms of arming for the Second World War."
But it was more difficult to identify other such moments, as it was "pretty rare to identify genuinely isolationist periods" of British history.
"There's certainly bits where Britain has tried to account for itself," he said.
"But it's never been able just to disengage from Europe. It's always been bound up with treaties and alliances that commit it in different ways to relationships in Europe."
In February, Cameron negotiated a deal with European leaders that would give Britain improved terms of membership in the 28-member EU, including opting out of the standard commitment that members must work toward "ever closer union."
The government's official position is that remaining in the EU under the improved terms of membership is in Britain's best interests, but many leading politicians, including high-ranking members of Cameron's own party, have been campaigning for a Brexit.
Polls show the public closely split over the issue.
Cameron calls referendum on EU membership