Britain's economy will be significantly damaged by Brexit's impact on immigration
But if there is a Brexit and, in turn, the government decides to restrict immigration, this could have "significant and damaging effects" on British companies and the economy because it would hurt one of the nation's main sources of workers - EU migrants.
That's according to a report, entitled "The impact of free movement on the labour market: case studies of hospitality, food processing and construction," published by the National Institute of Economic and Social Research on Wednesday (emphasis ours):
The report found that the frustrations employers experience attracting British workers to low-skilled jobs, and found there were few viable alternatives to EU migrants.
UK-born older workers and students had disadvantages in terms of their availability and suitability for the work required, while non-EU migrants were often over-qualified and their recruitment costly and time-consuming because of visa applications.
Despite some difficulties associated with poor English, a number of case study employers said they would not have been able to expand their businesses without EU migrants, and they formed part of their plans for future growth.
They blamed the negative image of their sectors and poor careers guidance for their lack of appeal to young British workers, although they also acknowledged that low pay, poor conditions and the often arduous nature of the work played a role.
Construction firms in particular said their industry would benefit from better training, but added that more government support was needed for this to happen.
Various polls over the last year or so have shown how the Freedom of Movement Act, which allows all EU citizens to easily migrate to any other member state, as well as immigration in general, is one of the factors that pushes UK voters to pip for exiting the EU.
After all, government data shows that net migration into Britain from the EU was 180,000 in the year to June 2015 - a new all-time high.
Freedom of Movement Act rules only apply to EU citizens - not asylum seekers, expats or economic migrants. However, of the 3.2 million non-UK nationals working in Britain in the third quarter last year, just under 2 million were EU nationals.
"A large section of the public would like to see significant restrictions on free movement, whatever the result of the EU referendum," said Dr Heather Rolfe, Principal Research Fellow at NIESR in a statement.
"But our research with employers in three key sectors leaves no doubt that restricting their access to this source of labour could have significant and damaging effects on many companies and the jobs of the British workers they employ. From the perspective of employers in low-paid sectors, free movement works pretty well. EU migrants are not a EuroMillions win, but they meet their needs."