Your Grace,
There have been a number of Project Fear Redux stories in the newspapers recently claiming that EU citizens are leaving or are planning to leave the NHS in droves and that
ipso facto there would be a strain on staffing levels.
e.g.
http://www.thenational.scot/politics/15661066.Brexit_fears_drive_doctors_from_the_EU_to_quit_the_NHS/
or
http://www.independent.co.uk/news/health/brexit-nhs-nurse-numbers-fall-first-time-years-a8032306.html
Whilst the figures I provided did NOT relate to EU employees specifically they DO show that staffing levels are going UP.
The latest figures I can find specifically for EU employees are here:-
http://researchbriefings.parliament.uk/ResearchBriefing/Summary/CBP-7783 which has a link to the NHS staff from overseas: full PDF report.
In terms of employment overall there has been an increase of nearly 50,000 EU Nationals in the last year, and looking specifically at EU8 workers, their numbers are higher than before last year's referendum (See today's ONS Labour Market Statistics)