Britain's future relationship with Europe is still uncertain after the overwhelming defeat of Theresa May's deal in Parliament on January 15th.
The worry for many British employers is that further messy negotiations and hostile political rhetoric will make it ever harder to attract skilled European workers.
A sharp decline in the number coming is visible.
Surveys of airport passengers show that net EU immigration in the 12 months to June 2018 added up to an estimated inflow of 74,000 people,
compared with 189,000 in the year before the June 2016 Brexit referendum.
But those figures do not make any distinction between skilled and unskilled workers.
An alternative approach is to look at data compiled by LinkedIn, a website that is used by more than 590m workers worldwide,
mostly well-paid white-collar ones, to share contact details and employment histories. All LinkedIn users record their location when they join.
These data can be analysed to measure the attractiveness of the British labour market in two ways.
First, they can be used to see if members in other countries are searching for jobs in London (the most attractive British city for overseas workers).
The numbers show a clear, but not catastrophic, decline in Britain's appeal.
London at the start of 2016 was the target of 15% of job hunts by workers from other countries in the EU; the proportion has since fallen to 12.6%.
Rival European cities, such as Amsterdam, Paris and Berlin, have all increased their share of job searches to compensate for London's decline.
But Europeans have not been discouraged altogether from moving across the Channel. London remains the most popular city for job searches.
Another way of looking at the numbers is to see how many LinkedIn members move to a new country (this relies on the workers updating their profiles).
On this basis, there was a fairly sharp, 10% decline in the number of EU citizens shifting to Britain in 2017, followed by a rebound back to 2016 levels last year.
But the fall and rebound are not adjusted for the fact that LinkedIn membership has increased by over a quarter since 2016.
Britain has lost "market share" of skilled immigration, attracting 20.8% of intra-EU moves in 2018, down from 23.6% in 2016.