A report from think tank Open Europe states that "there is growing evidence that there would be a small negative economic result from Brexit, probably in the region of 0.5 - 1.5 per cent". And that's presuming a "reasonable trade agreement is struck between the UK and the EU".
As well as that, Open Europe thinks that net immigration is unlikely to reduce.
Read more: Why are EU citizens coming to the UK?
It cites the business case for maintaining a flexible supply of labour, the political and economic challenge of finding alternatives to relieve pressure on public finances caused by ageing demographics and the effects of globalisation on migration flows.
But importantly, it also states that there is likely to be constraints on the UK's immigration policy under a new arrangement with the EU.
That's been a contested area in the upcoming EU referendum, with the Leave camp stating that the UK could take control of its borders and set up a free trade agreement without free movement, while the Remain camp points to countries such as Norway, which have accepted free movement in order to access the single market.
"There is likely to be a trade-off between the depth of any new economic agreement with the EU and the extent to which the UK will have to accept EU free movement. The evidence from the precedents of Norway and Switzerland suggest that the deeper the agreement, the more likely the UK will need to accept free movement," says Open Europe.
Yet the think tank adds that a more selective policy, geared at skilled migrants, could work politically. That could allow UK industries suffering skills shortages. Still, there would need to be a mechanism for low skilled jobs to meet labour shortages.
And just to put the UK's immigration in perspective: Between 2000 and 2015 the UK received 3.7 migrants for every thousand people, which puts it just above the average but below countries such as Canada, Australia, Norway and Switzerland.
If the UK had experienced the same level of immigration as Canada or Australia there would have been an additional 3m or 4.4 million migrants respectively coming to the UK over the past decade – though of course the UK is a more crowded country, Open Europe said.