According to a new report from independent think tank British Future, most Leave voters would support skilled migration from the EU remaining at the same level as now or even increasing, while half of Remain voters support reductions in low-skilled EU migration.

Polling by ICM found that 86% of the public want high-skilled EU migration to stay at the same level as now or increase (48% stay the same, 38% increase) after Britain leaves the EU. And 82% of Leave voters would be happy for high-skilled migration to stay the same (51%) or increase (31%).

The public would, however, prefer reductions in low-skilled immigration: 64% of the public, including 50% of Remain voters, say they would like low-skilled EU immigration numbers reduced, with 36% happy for them to stay the same or increase (31% stay the same, 5% increase).

In its new report, Time to get it right: Finding consensus on Britain’s future immigration policy, British Future proposes a new post-Brexit immigration system which reflects this consensus, combining greater UK control over low-skilled migration with the needs of business and public services for immigration. Nearly two-thirds of the public (63%) would support a new system which offers control of low-skilled immigration through an annual cap while allowing skilled migrants to come to the UK as before, including 71% of Leave voters and 60% who voted Remain, as well as 75% of Conservatives and 57% of Labour voters. Just 14% of the public said they disagreed with the proposal.

Findings on attitudes to immigration by profession also show public support for skilled immigration. Most people would prefer the amount of migration from doctors and nurses, scientists and researchers, engineers, IT specialists and business and finance professionals to stay the same or increase.

People also make allowances for people doing certain lower-skilled jobs that need filling: some 75% want the number of care workers to either stay the same or increase; with majorities also happy for numbers of EU construction workers (63%), waiters (52%) and fruit-pickers (63%) to stay the same or increase.

The ICM research finds 63% of the public agrees that ‘The government should replace the net migration target with separate targets for different types of immigration, like skilled and low-skilled workers.’ Seven in ten (72%) Conservative voters agree that the net migration target should be replaced.

ICM surveyed 3,657 GB adults online between 9-14 June 2017 for this report, with boosted panels of 1,052 in Scotland and 527 in Wales.