EU workers should be given “no preference” for visas to come to the UK after Brexit, says a new report.
The Migration Advisory Committee also recommends that it should be easier for higher-skilled workers to migrate to the country.
It has called on the government to scrap a limit on high-skilled workers altogether – currently 20,700 each year for those from non-EU countries.
The government has said it will “carefully consider” the proposals.
Labour backed the report, calling for an “end to discrimination” against non-EU migrants.
The MAC was asked to do the research in July 2017 by then Home Secretary Amber Rudd. It is thought the report will shape the government’s post-Brexit immigration policy.
The report made 14 proposals after analysing the impact of migration from the European Economic Area (EEA), taking evidence from more than 400 businesses, industry bodies and government departments.
The committee said it did “not see compelling reasons to offer a different set of rules” for workers from the EEA.
The report said: “If the UK is in a position where it is deciding the main features of its immigration policy, our recommendation is that there should be a less restrictive regime for higher-skilled workers than for lower-skilled workers in a system where there is no preference for EEA over non-EEA workers.
“Higher-skilled workers tend to have higher earnings so make a more positive contribution to the public finances.
“The estimated labour market impacts, though small, also suggest that higher-skilled workers are of greater benefit as do any impacts on productivity and innovation.”
The committee said it was “not convinced there needs to be a work route for low-skilled workers” from the EU to fill jobs in industries such as catering or hospitality.
It admitted that some sectors would “complain vociferously about being faced with an alleged cliff-edge in their supply of labour”.
But it believed, even with no new route, the number of existing low-skilled migrants would not change immediately and there would likely be a continued flow coming over to live with family.
The “possible exception” to this rule would be for seasonal agriculture, where 99% of the workers come from EU countries.
The BBC’s assistant political editor, Norman Smith, said the report would increase pressure on Theresa May to not compromise over freedom of movement during the Brexit negotiations.
He said: “Mrs May has so far repeatedly refused to rule out granting EU citizens some form of preferential access.
“Any such move, however, would be likely to further enflame opposition among anti-Chequers MPs [those against her existing Brexit plan].”
The government reiterated the importance of EU citizens working in the UK.
A Home Office spokeswoman said: “After we leave the EU, we will take back control of our borders and put in place an immigration system that works in the interests of the whole of the UK.
“We commissioned this report in addition to our engagement with business to better understand the impact of EU citizens on the UK labour market.
She added: “The government is clear that EU citizens play an important and positive role in our economy and society and we want that to continue after we leave.
“We will carefully consider the Migration Advisory Committee’s recommendations before setting out further detail on the UK’s future immigration system.”
Shadow Home Secretary Diane Abbott said the government should not ignore the report.
“Labour has said that our immigration policy needs to be based on our economic needs, while meeting our legal obligations and treating people fairly,” she said.
“[This] means ending the discrimination against non-EU migrants, especially from the Commonwealth.”
It comes as latest figures showed that net migration from the EU was at its lowest level since 2012 – with the number of EU citizens coming to look for work down by a third to 37,000 and overall net migration at 282,000.
The government wants to cut overall net migration to the tens of thousands.
The Migration Advisory Committee has already suggested that international students in the UK should not be removed from targets to reduce migration.
Last month, the Confederation of British Industry said net migration targets should be scrapped after Brexit and replaced with a system that ensures people coming to the UK make a positive contribution to the economy.