Latest statistics suggest a fall in net migration and a big drop on EU workers coming from the eight so-called accession countries (A8) like Poland.
More than 100,000 EU citizens have left Britain - 17% more than in the previous year. And arrivals from the A8 countries have fallen sharply. The number of new registered workers from Poland is down 16% year on year, Hungary is down 14%, Slovakia down 20% and Lithuania down 6%.
Uncertainty over the status of EU citizens in a post-Brexit Britain, and the sharp fall in the exchange rate of the pound, has made the UK a much less attractive prospect.
The tourism and hospitality sector, for instance, has relied upon importing foreign labour. A quarter of hospitality businesses across Britain say they currently have vacancies they are struggling to fill. York, where the tourist industry is booming, it is now worth an astonishing £500m a year and supports more than 20,000 jobs. But the expansion could not have happened without immigration. The city has close to full employment - there are estimated to be fewer than a thousand local job seekers. The news of a fall in migrant workers from countries which have traditionally filled tourist jobs makes grim reading for York's hoteliers, restaurateurs and bar owners.
If the numbers continue to fall, some fear the worst. "It would create a staffing crisis," says Graham Usher, who heads York's Hoteliers' Association. "If we get to the point where we can't fill vacancies with European workers then there's a big gap that we just can't fill."
It is not just the tourism and hospitality sector, of course. Britain's record employment rate means there is often no immediate domestic alternative to migrant labour for many businesses looking to expand or simply survive.
Poskitt's Carrots is a £35m a year business in the East Riding of Yorkshire, supplying vegetables to many of Britain's big supermarkets. “If we didn't have access to non-UK labour we just could not run this business," says managing director Guy Poskitt. "I wouldn't even attempt to try and run it. Take away 80% of my workforce how can I operate?" Guy Poskitt doesn't want to be reliant on migrant labour, but argues that there just aren't the domestic workers available from the rural communities nearby.