Those backing a "Brexit" -- Britain leaving the European Union -- say the country should have better control of who comes in.
One of the central pillars of the European Union is the free movement of labor, which essentially means any citizen from the other 27 countries in the bloc can turn up to Britain and look for work without a concrete job offer.
Many Brexit supporters say this is the reason for the country's levels of net immigration -- the number of people migrating to the country minus those who leave. Net migration reached a near-record 330,000
in 2015, according to the Office of National Statistics, numbers that have been used to strengthen the leave camp's position, fanning the flames of growing anti-immigration sentiment.
But the remain camp says the Brexiteers are simply fear-mongering.
The number of non-EU immigrants to Britain is actually slightly higher than immigrants from the European Union, and the statistics office described the change in overall immigration as not significant. It said the small increase in net figures was because fewer Britons left the country, rather than a spike in people coming in.
What could a new immigration system look like?
High-profile pro-Brexit campaigners propose an "Australian-style points based immigration system" if the country chooses to leave the European Union.
"The automatic right of all EU citizens to come to live and work in the UK will end, as will EU control over vital aspects of our social security system," it said.
The idea of a points based system is that certain skills and qualifications are worth more than others to an economy. The more in demand the skill is, the more points a prospective immigrant will get. Those who reach a threshold would be eligible for a visa.
This allows countries to tailor immigration to their needs. For example, Australia is currently accepting more skilled chefs, mechanics, architects and nurses,
because it doesn't have enough of them.
The Vote Leave campaign's statement said there would be no changes for Irish citizens, as their rights to reside and work in Britain are already protected in the law.
There would be no change for EU citizens already lawfully resident in the country, either. "These EU citizens will automatically be granted indefinite leave to remain in the UK and will be treated no less favorably than they are at present," it said.
Britain already uses points and criteria for some visas given to non-EU immigrants, and the statement did not make clear whether the proposed system would differ.
Ironically, the points system, also used by Canada and New Zealand, was designed to increase immigrant numbers in countries hoping to expand their economies, not to reduce numbers of people coming into a country.
Will Brexit reduce migration?
Critics of Brexit warn that leaving the European Union will not automatically reduce migration.
Some of it depends on whether Britain wants to continue free trade with the European Union. If it does, one option is to remain in the European Economic Area (EEA), which would allow the country access to the EU's single market. This is the case for Norway, Iceland and Liechtenstein. Switzerland is also part of the single market, even though it's not an EU nor EEA member.
The catch is, staying in the EEA means Britain would have to keep free movement of labor -- so immigration wouldn't change at all.
If it pulls out of the EEA, some economists say trade deals would need to be renegotiated and that European nations scorned by Britain's departure may not be forgiving. They could make immigration demands in return for free or favorable trade.
This is where most economists say the biggest cost of Brexit could lie. If Britain stays in the EEA, little will change economically. But leaving will create uncertainty and outcomes will depend on what the government can negotiate, they say.
But a campaign group called Economists for Brexit says that trade deals are simply not needed. Britain's largest trade partner is the United States, and the two countries don't have a deal -- they simply do business under World Trade Organization rules. This is the same for trade with China, Britain's fourth-largest trading partner.
Is EU immigration really a problem?
The government has come under pressure to reduce the flow of people moving to the country and a year ago set a net immigration target of 100,000, less than a third of the current number.
Among arguments by Brexit supporters are that immigrants are putting too much pressure on public services, like the country's National Health Service, and social welfare benefits. Some Britons, mostly those in lower-skilled jobs, are concerned about losing employment to Europeans.
Neil McKinnon, from Economists for Brexit, said the economic arguments made by the remain camp had been grossly overstated and that the overarching argument for Brexit is simply to take back control from Brussels. That includes immigration policy.
"In the same way that America would like better control of its borders, there are a whole variety of reasons, such a security, that makes it imperative for us as a sovereign state to have control of our borders," he told CNN.
"There is a feeling that free movement discriminates against non-EU migrants from countries that had previous ties with the UK," McKinnon said, adding that a points based system has worked well for Australia, Canada and other countries.
On the other side of the fence, economists supporting Britain remaining in the European Union, say concerns on immigration levels have been overblown.
Ian Preston from the University College London's Department of Economics said there is no need for a cap on immigration because the market naturally controls how big the labor market will get.
"It's quite simple. When the economy is doing well, people will come in higher numbers for work, and when it slows, you will see those numbers drop," Preston said.
"The evidence shows that in the past 15 years, immigrants -- and EU immigrants in particular -- pay more to the state in taxes than they take in public services.
"Immigrants have proved to be less dependent on public services than British-born workers. They make less use of health services, they have lower rates of crime and they usually come already educated," he said.
He also questioned the government's net migration target of 100,000, saying it was essentially a made-up figure that had no proven economic benefits, and that even if EU migration was reduced to zero, Britain would still have to reduce the 188,000 immigrants, in net numbers, that came from outside the European Union in 2015.
Polls show that a week out from the once-in-a-generation referendum, so many people are still undecided on how to vote that they alone could determine the outcome. Many in the public have complained that the debate has been confusing, with different data being used by each camp to suit their purposes.
"There's been quite a lot of nonsense spoken on both sides," said Rob McNeil of the Migration Observatory, an impartial body at Oxford University.
"'Facts' have been used by both sides that don't necessarily stand up. The entire debate on numbers and control of migration has been built on sand," he said.
"We don't know what the government will do with the immigration system if it leaves the EU, but we certainly can't say it would reduce migration without having significant, profound economic costs."