Immigration would be unlikely to fall significantly if Britain left the European Union, according to a report by the free market thinktank Open Europe.

Clamping down on immigration is one of the central arguments of leave campaigners in the run-up to the 23 June referendum on whether Britain should remain in the EU.

But in a report titled “Where next? A liberal, free market guide to Brexit,” Open Europe points out that other large, developed economies with low unemployment tend to attract high levels of immigration, even without espousing the EU principle of free movement.

“We don’t think immigration is likely to be reduced that much outside the EU, despite the political pressure,” said the thinktank’s co-director Stephen Booth. “The UK is not alone in experiencing quite high levels of immigration.”

Between 2000 and 2015, he pointed out, the UK received an average of 3.7 migrants per 1000 of the population each year. The average for members of the Organisation for Economic Co-operation and Development – in general, the large, industrialised countries – was 3.1.

He added that Canada, Norway and Switzerland, all countries sometimes highlighted by Brexit campaigners as representing a model for a better relationship with the EU, have all experienced higher levels of net immigration.

Booth’s co-director, Raoul Rouparel, said: “if you’re a medium-sized, developed economy with very low levels of unemployment, you’re going to experience high levels of immigration.”

Open Europe analyses the steps Britain could take to change its immigration rules in the wake of an exit from the EU – adopting a points-based system to focus more on skilled workers who are needed in particular sectors, for example.

But it argues that an influx of low-skilled workers would still be necessary to feed the demands of the labour market. And it adds that imposing limits on the rights of EU citizens to live and work in the UK would have a likely cost in negotiations over future trade deals, as other EU states would probably want to restrict access to the single market as a quid pro quo.

As a post-Brexit Britain sought to negotiate new trade deals with fast-growing emerging economies such as China and India, they too may increasingly demand more favourable visa regimes or other ways to allow their citizens access to the UK, Open Europe suggests.

Immigration is just one area where Open Europe suggests policymakers would be forced to make difficult trade-offs if the voters choose to leave the EU after June, which have so far received little attention in the public debate.

“Brexit will not be an economic disaster and it will not be a utopia. There are tough choices involved – nothing comes for free,” said Open Europe’s chairman, Lord Leach of Fairford.

It says the economic benefits of cutting loose from Brussels and slashing regulation could only be achieved by a government that was willing to sacrifice the rights of workers, enshrined in legislation such as the Agency Workers Directive; and to unleash the “creative destruction” that would come with tougher competition.

“If you left the EU, the trend would be further liberalisation, further globalisation, if you want to make it a success,” said Booth. Ruparel added that stripping away support for agriculture, for example, would be likely to unleash “creative destruction”, which could make the agricultural sector leaner and more competitive – but only by forcing hundreds of farms out of business.

Labour leader Jeremy Corbyn will make the left-of-centre case for Britain to remain in the EU in a major speech on Thursday; but Open Europe’s analysis supports the view of other senior Labour figures, including Ed Miliband and Tom Watson, who have argued that a post-Brexit Britain could leave workers and struggling firms with less protections.