The vast majority of Leave voters would accept the migration of high-skilled EU workers remaining at current levels or increasing, new research has revealed.
A poll found 82% of Brexit supporters would be happy for high-skilled EU immigration to remain at current levels and 31% would not oppose it increasing.
The survey, by think tank British Future, also found half of Remain supporters back a reduction in the numbers of low-skilled workers arriving from the EU.
"A new post-Brexit immigration system that differentiates between skilled and low-skilled EU immigration sounds like common sense to most people," Sunder Katwala, Director of British Future, said.
The Government's plans for a post-Brexit immigration system have come under intense scrutiny since the referendum last June, when the matter was central to debate.
Fresh details of the Government's immigration policy are due to be unveiled in the autumn.
Figures published last month showed net long-term migration to the UK is at its lowest level for three years and the rate of EU nationals leaving the country increased. The Office for National Statistics said the figures indicated the 2016 Brexit vote "may" be having knock-on effects on migration.
The British Future study, based on a survey of more than 3,600 people, suggested concern with immigration numbers is focused primarily on low-skilled migration.
Nearly two in three respondents (64%), including 50% of Remain voters, expressed a preference for a reduction in immigration from the EU for low-skilled workers.
Mr Katwala said: "There is public support, across political and referendum divides, for an immigration system that combines the UK control demanded in the referendum with openness to the migration that our economy will continue to need."