Theresa May’s attempt to reclaim control of UK borders after Brexit could reduce annual migration from the EU by just 50,000 – one-sixth of the current overall annual figure, according to new research.

The projection of a “vanishingly small reduction” is one of the first attempts to estimate how likely labour market demand, and the government’s planned new controls, could reduce the number of migrants coming to the UK. Reduction in immigrant numbers has been repeatedly cited in polls as the chief reason voters backed leaving the European Union.

The report by a new thinktank, Global Future, shows total net immigration, which at the latest official estimate was 335,00 in the year to June 2016, could be expected to fall by no more than 15%, to 285,000 a year. Future free trade deals with non-EU countries suggests even this reduction could be wiped out.

Liam Fox, the international trade minister, accepted last week he did not know of any new free trade deal that did not also include liberalisation of migration rules between the two countries signing such agreements. Australia and India have already indicated they will seek preferential access for their workers as part of a free trade deal.

The government has so far refused to produce its own estimate of the cut in migration from Brexit, or precisely how new controls will operate. But the report’s estimates, which were formulated by breaking down the different elements of net migration from the EU and examining government commitments to retain skilled labour, students and some seasonal work, represents one of most thorough projections to date.

The report argues: “While ending freedom of movement is psychologically appealing to those who want a sense of control of our borders, the reality is such a move would create more the illusion of control. People looking for substantial reductions are likely to be disappointed with the eventual figure of 50,000 or less.”

The thinktank has won the backing of the Sainsbury’s chief executive Mike Coupe, as well as Liberal Democrat leader Tim Farron.

Its director, Gurnek Bains, said: “The extent to which this impact is worth the myriad of economic and political problems that pulling out of free movement would create needs to be reflected upon. In addition, promising more than can be delivered on migration risks creating a firestorm in the future.”

Farron said: “In return for this self-inflicted wound it is unlikely that the Conservative Brexit government will be able to deliver its promise of dramatically reduced immigration.”

The report starts with the premise that the current true net immigration figure from Europe is 182,700 annually, representing the maximum amount of reduction possible from leaving the EU out of a total immigration figure of 335,000.

The estimates suggest net migration of EU students will be unchanged post-Brexit, even though the mix of EU and non-EU students may shift. It also suggests the currently small number of EU citizens coming mainly for family or marriage reasons will remain constant at 25,000. This route will become one of the most attractive way of entering the UK, the report points out.

In the biggest category, the number of workers coming in from the EU, the report projects a fall from 204,000 to 125,000, citing government indications that it would have to exempt key professional staff and ensure employers continued to have a ready supply of labour.

Even this modest decrease, however, is likely to be offset by EU citizens already in the UK being less likely to leave Britain and the prospect of restrictions on UK citizens moving to other countries in the EU.

The report points out 22% of EU migrants are in professional jobs, 22% in skilled occupations and 56% doing unskilled jobs. The UK has already said it will need to keep the professional route open, so the report assumes 50% of existing flow professional workers will still be required.

Ministers have also said they will respond to employer pressure to meet their demand for 80,000 seasonal workers, 90% of whom come from the EU.

The report then looks at the large proportion of workers in the key industries such as hospitality, transport and building. “Complete closure of the skilled and unskilled categories is simply not feasible without catastrophic consequences for a range of UK sectors,” it warns.

The thinktank points out that in its recent Brexit white paper, the government itself also conceded that the supply of skilled and unskilled workers cannot be switched off without serious disruption to key industries. It has promised to work closely with business leaders to ensure adequate supply of labour for key industries.

The report also looks at the number of the EU citizens in the UK returning to the EU, saying the number will fall from 95,000 to 58,000, partly due to fears they will be unable to return to the UK. It also expects the current small net outflow of UK citizens to Europe will fall to zero, partly due to changes to residency requirements, access to healthcare and taxation for the estimated 1.2 million UK citizens who live in Europe.

Critics will say the thinktank set up to break down cultural barriers has had to make too many assumptions and does not take into account the public’s support for the principle of controlling borders.