British Justice Secretary Michael Gove, a prominent Vote Leave campaigner, wrote in a column in British newspaper The Times
on Monday that the country faced an immigration "free-for-all" if it remained in the EU.
He warned that the potential growth of the bloc to other countries seeking membership would result in millions more people gaining the right to move to the UK.
"Because we cannot control our borders, public services such as the NHS will face an unquantifiable strain as millions more become EU citizens," he wrote, referring to the National Health Service.
"We cannot guarantee the same access people currently enjoy to healthcare and housing if these trends continue. There is a direct and serious threat to our public services, standard of living and ability to maintain social solidarity if we accept continued EU membership."
But the move to focus on immigration has drawn criticism from their opponents, with one former Cabinet minister -- Peter Mandelson -- accusing the Vote Leave campaign of straying into "nationalist territory."
Focus on immigration
Campaigners on both sides of the debate are making their arguments to the public ahead of a June 23 nationwide vote on whether to leave or remain in the EU.
The British government says it believes voting to stay in the 28-member bloc is in the country's best interest, as does Prime Minister David Cameron.
But senior members of Cameron's Conservative Party -- including members of Parliament Iain Duncan Smith and Owen Paterson -- are backing the Vote Leave campaign and have increasingly focused their arguments on immigration.
In a speech Monday on the future of Europe, Paterson warned about the EU's migration effects on Britain, saying the bloc would soon have five more countries and 87 million more people.
In particular, he warned of the potential inclusion of Turkey, which is also in lengthy negotiations to join.
"Turkey, led by an increasingly authoritarian regime, has a 700-mile-long border with war zones in Syria and Iraq," he said.
"The implications for European and British security are all too plain."
He also warned of predictions Germany could have more than 3 million refugees by 2020 -- many of whom could then acquire EU passports and potentially move to the UK.
Strain on hospitals cited
Citizens of EU countries have the right to live and work in other countries in the union, and many have come to the United Kingdom, attracted by a relatively strong economy.
Official statistics show about 632,000 people moved to the UK in 2014, nearly double the number of people who left the country.
The British government estimates that about 1.2 million British people live in other EU countries, while 3 million people from other EU states live in the UK.
Just under half -- about 48% -- of immigrants to the UK hail from EU countries.
Campaigners for the so-called Brexit, or British exit from the union, say that the net migration gains of more than 300,000 people annually has placed a dangerous strain on the country's public resources such as the National Health Service.
The Vote Leave campaign says that "rising demand" for NHS services is one of the key factors identified by administrators for its forecast £2.4 billion ($3.5 billion) deficit for the past financial year.
The strain on health services is also criticized by Migration Watch UK, which describes itself as an independent and nonpolitical think tank.
The group argues that immigration to the UK, which has a population of about 65 million, is "neither sustainable nor well managed," and is also straining education services, fueling a housing shortage and occurring at a rate that prevents effective social integration.
Vote Leave hoisting 'white flag,' say rivals
The push on migration issues comes after days of media coverage over the potential risks to the UK's economy from a Brexit following President Barack Obama's comments on the matter
during his visit last week.
The move to focus on migration issues was slammed by anti-Brexit campaigners Stronger In, drawing accusations that the Vote Leave campaign had strayed into "default nationalist territory" out of desperation.
Mandelson, a former Cabinet minister and European commissioner, said that resorting to arguments about immigration showed that pro-Brexit campaigners had "hoisted the white flag on arguments around the economy."
"First the Treasury then Barack Obama demolished their flimsy arguments about trade and prosperity and so they have turned instead to their default nationalist territory of immigration," he said in a statement.
The London School of Economics said last month that reduced income from trade in the event of a Brexit would cut average household income by at least £850
($1,232) a year.
Mandelson accused Vote Leave of "now running a UKIP-lite strategy" -- a reference to the right-wing populist UK Independence Party, or UKIP, which campaigns strongly against immigration.
Polls have shown the British public narrowly divided on the issue, with the latest YouGov survey finding 40% in favor of remaining, 39% in favor of leaving and 16% undecided.