Only a bespoke workforce deal with the EU would allow the public sector to recruit top-end talent as well as sufficient numbers of skilled workers and lower-skilled staff, according to finance chiefs.
The Brexit Advisory Commission for Public Services, set up by CIPFA, says only one of the options currently being considered for a future relationship with the EU would meet the public sector's needs.
It says a workforce deal with the EU would need to be flexible enough to ensure public sector organisations can recruit the talent they need and recruit the best international talent.
This would include medical professionals and academics as well as lower-skilled staff including care workers.
CIPFA says any new deal must be flexible, 'consistent with the likely funding level of public services' and avoid unnecessary bureaucratic barriers.
The commission's chair Julia Goldsworthy said: 'Even though we haven’t yet left the EU, there has already been a negative impact upon the health and social care workforce.
'Considering a drop in EU migration would directly affect public services, the UK government must not decide upon their approach to the workforce settlement without seriously taking stock of how best to support the public sector. 'Our evidence suggests that a bespoke deal seems like the best option available, and so we hope this is pursued.'
