Britain publishes proposals for an EU immigration crackdown after Brexit on Wednesday as business groups warn the economy is not ready for Britain to crash out of the European Union without a divorce agreement in place.
Home Secretary Sajid Javid said visas would be introduced for EU nationals arriving after Britain leaves the bloc and the new system would be based on skills, not nationality, putting EU and non-EU citizens on the same footing.
"It will be a system that will bring net migration down to more sustainable levels," he told BBC radio, although he said there was "no specific target" for the reduction.
He said he hoped the new measures would put more pressure on employers "to look at the domestic workforce first".
Javid did not commit to an annual salary threshold for EU immigrants - a highly contested proposal - but said it could be "30,000 pounds (USD 38,000) or thereabouts".
He said the threshold could be lowered to encourage foreign students to stay and work in the UK and for certain parts of the economy in which a labour shortage could be proven.
Many employers, including the National Health Service, have warned that 30,000 pounds is too high and will severely limit their ability to hire EU nationals such as nurses.
But they will cause anger in parts of Britain, such as London, that have benefited from EU immigration.
Mayor of London Sadiq Khan said the government's approach was "misguided" and "risks doing profound damage to growth, jobs and communities across London and the UK".
May has vowed to end free movement of people from Europe, saying that this was one of the main reasons that Britons voted to leave the European Union in a 2016 referendum.
Immigration levels have already fallen since the referendum.
Net migration to Britain was around 280,000 last year, a decrease from levels of more than 300,000 in 2014 and 2015.
The announcement came as May prepared to hold her final question and answer session of the year in parliament, where she will face more trenchant criticism of her decision to delay a parliamentary vote on her Brexit deal.
The main opposition Labour Party has asked for a no confidence motion against May, while smaller groups including the Scottish National Party have requested a similar vote against the government as a whole.
Neither motion is expected to be allowed to come to a vote.
May survived a separate no-confidence vote tabled by members of her own Conservative Party last week but she came out of the process badly bruised after more than a third of her parliamentary party opted to oust her.
Some hardline Conservative MPs have since said they could vote in favour of May's deal when it comes before parliament next month, although experts say the vote is still likely to go against the prime minister.
The deadlock in Westminster has raised the prospects of either a second referendum or of a no-deal Brexit when the negotiating time runs out on March 29 next year.
The government on Tuesday announced no-deal plans, which include drastic measures such as stockpiling imported chemicals to ensure safe drinking water and special flights from Europe to ensure continued supply of vital medicine.
The prospect of such an exit has caused widespread concern.
Britain's five leading business associations on Wednesday warned that companies have been "watching in horror as politicians have focused on factional disputes rather than practical steps that business needs to move forward".
The group, which included the Confederation of British Industry big business lobby and the Federation of Small Businesses, said: "The lack of progress in Westminster means the risk of a no-deal Brexit is rising".