John O’Keefe, the UK’s latest Nobel Prize winner, has a lot in common with Venki Ramakrishnan, the next President of the Royal Society.

First, they are similarly brilliant scientists and Nobel Laureates. O’Keefe was a joint winner last year for his discovery of cells that act as our inner GPS system, enabling us to know where we are and navigate around our environment. Ramakrishnan won his Nobel Prize for his work on the structure and function of the ribosome – a biological machine that makes proteins in our cells.

Secondly, they are both immigrants whose enormous contribution to UK science was only possible because they chose to adopt the UK as their home.

These are two very eminent examples of a much bigger point: UK science is only as good as the people in it. Part of the reason for the UK’s global success in these fields is our current and historical ability to attract the world’s most talented minds.

And it's not just Nobel Laureates – around one in 10 UK academics comes from outside the EU. They are developing their research in our universities while also training the next generation of British scientists and engineers. That’s not to mention the talented foreign scientists and engineers working in companies up and down the country.

Science is an increasingly global and interconnected endeavour – and that brings enormous benefits. But the direction UK immigration rhetoric and policy is going risks putting an artificial cap on scientific progress and economic growth. Just this week David Cameron has unveiled a new crackdown on non-EU workers – including skilled workers.

The government wants companies who recruit from outside the EU to put more effort into training up British workers in areas where there are skills shortages. And while getting more young people in the UK interested in these subjects can only be a good thing, it won't compensate for the "crack down" on the number of talented people who can study, work or live in Britain.

Looking at skilled workers, John O’Keefe has described immigration rules as a large obstacle to recruiting the best people. Talented scientists or engineers are in high demand around the world, and in many countries they’ll be welcomed with open arms rather than bombarded with messages telling them to go home.

Policies and public debate on immigration are complex. Throw in questions around the EU and it is ever more so. But if immigration policy continues in the current direction, achieving the government’s aim of making the UK the best place in the world to do science could be an impossible task.