Boris Johnson should adopt a "balanced" approach to handling immigration as public interest in the issue wanes, a top think tank has suggested.
A report from British Future found immigration has dropped to the ninth most important issue for voters with some 63% calling for more flexibility to allow nurses and care workers to come to the UK.
It comes after the Home Office unveiled its new 'Australian-style' points based system to control migration after Brexit.
Under the plans, migrants will be expected to speak English, have already been offered a job in the UK, and have a clean criminal record.
Meanwhile, the minimum salary threshold for jobs offers will be £25,600.
But an ICM poll for the study found agreement across the political spectrum for flexibility in those requirements when it comes to health care staff, with agreement from 62% of 2019 Conservative voters and 67% of Labour voters.
A majority (58%) of Leave voters also agreed with the plans, while 73% of Remain voters also were in favour.
The figures show a marked change in attitudes among the public with the NHS and Brexit coming "top of the mind" when voters were casting their votes in the December general election, with immigration dropping from the number one issue during the 2016 referendum to ninth.
However, the poll found a slim majority (51%) were still in favour of reducing low-skilled EU migration after Brexit, although 64% would like to see the number of international students coming to the country to either remain the same or increase.
British Future director Sunder Katwala said the poll showed Boris Johnson could take a "pragmatic" approach after ditching the failed net migration targets championed by Theresa May.
"Boris Johnson has an opportunity now to bring more light and less heat to the immigration debate – because of how attitudes have changed since the 2016 referendum" he said. "With the debate now more open, people can't really claim they're not allowed to talk about immigration. The question is what choices we should make.
"This research confirms that most people are 'balancers' on immigration, wanting to manage the pressures better and to keep the gains too.
"Without the millstone of the net migration target around his neck, the Prime Minister can make his case that taking back control should mean Britain welcoming the migration we decide to keep."
Meanwhile, Professor Bobby Duffy, the director of the Policy Institute at King's College London and co-author of the study, said: “It's often imagined that the public can be divided into groups that are either utterly in favour of immigration or dead set against it.”
“This study shows that most are in the middle, with views that depend on the type of immigration you are talking about.”
He added: “Those views have also shifted over recent years, with a particular drop in how immigration ranks in peoples' minds. This provides a great moment to reset our approach.”