The Conservatives have set out more details of their plans for immigration after Brexit, saying migrants will be treated equally regardless of where they come from.
The cost for migrants to use the NHS would also rise, while the rules on claiming benefits – which currently favour EU nationals – would change.
The Tories say they want the “brightest and best” from around the world.
But business leaders say they need access to workers of all skills levels.
Labour is yet to announce its immigration policy, but it is expected to be released in the party’s manifesto on Thursday.
And the Lib Dems are pledging a “fair, effective” immigration system if elected – with plans to resettle 10,000 unaccompanied refugee children a year.
The Conservative government has already promised that, after Brexit, immigration rules would apply to EU nationals and non-Europeans in the same way.
Earlier this week, party leader Boris Johnson also said that if he won the election, he would try to reduce the number of so-called “unskilled” migrants coming into the UK.
Announcing more details of their immigration policy on Sunday, the Conservatives said freedom of movement – which lets EU citizens travel, live, study and work in any member country – would end in the UK in January 2021.
The “vast majority” of migrants would need a job offer to come to the UK to work – although there will be a “small number of exceptions” for example high-skilled scientists.
Rules on claiming benefits will be “equalised”, meaning that like other migrants, EU citizens would have to wait five years before they can access benefits and will not be able to send child benefit payments abroad.
And the immigration health surcharge – the payment charged to migrants to use the NHS – would apply to all migrants, both EU and non-EU, and would be raised from £400 to £625 a year.
“As we come out of the EU we have a new opportunity for fairness and to make sure all those who come here are treated the same,” said Mr Johnson.
Home Secretary Priti Patel added that after Brexit, “immigration will finally be subject to democratic control, allowing us to get overall numbers down”.
Meanwhile, writing in the Mail on Sunday, Michael Gove said it was “unfair that people coming from European countries can access free NHS care without paying in while others make significant contributions”.
“Our country is made stronger by welcoming people with talent from across the globe,” he added.
“But it’s not right that people from Bulgaria and Slovenia can come here without any controls and have automatic rights that people from Bangladesh and Singapore do not.”
‘All skill levels needed’
Responding to the plans, business leaders said it was important that companies still had access to the workers they needed.
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Matthew Fell, from the Confederation of British Industry, said there was “concern that the focus of a new system is so squarely on skills”.
“The UK has labour shortages that must also be filled,” he said.
“A new approach must be just as open to workers who pick, process and transport the food we eat as the architects needed to build new homes and schools,” he said.
“Business and government need to work together to train UK workers while developing an open but controlled immigration system that grows our economy.”
Meanwhile, Hannah Essex from the British Chambers of Commerce said “access to skills at all levels is essential”.
A “flexible and simple immigration system” is needed that “allows firms to recruit the people they need at all skills levels, including temporary, seasonal and permanent roles,” she added.
The head of the Food and Drink Federation, Ian Wright, also called for an immigration system which “ensures easy access to the workers we need, at all skill levels”, while Tom Ironside, from the British Retail Consortium, said any immigration system must ensure the industry was “able to access workers across all skills levels in sufficient numbers”.
The Conservatives say they would introduce an Australian-style points-based system, which would consider migrants’ skills and whether they meet certain criteria.
In recent years, the party had a long-standing goal – first introduced by David Cameron and also a promise in the 2017 election manifesto – to cut net migration to less than 100,000 a year.
But the government never came close to meeting the target and faced repeated calls to drop it.
When draft proposals for a new immigration system were published last year, the target of 100,000 was left out.
Earlier this week, Ms Patel said the Tories would “look to reduce the numbers” of immigration through better controls but would not set “arbitrary” targets.
Labour has yet to announce its policy on immigration.
But Jeremy Corbyn has said he would commit to “a fair immigration process that recognised the huge contribution made by migrant workers to this country”.
“We have got to be realistic about the needs of our economy for bringing workers in, skilled workers in to help us,” he added.
An SNP spokesman said earlier this week that cutting immigration would be “hugely damaging” for the Scottish economy and called the issue to be devolved to the Scottish government.