I'm going to make the point leave that Schools and hospitals are not adveresely effected by EU immigration.
Oxford University found that actually an increase in EU immigrants lowered waiting times at local hospitals and for GP appointments. Usually because they are young and don't go to the Doctor that often.
The schools issue has been known about for years, and the government have failed to build enough new schools in places where they are needed, whilst at the same time funding free schools in areas where there are surplus places.
Then when you add the fact that 85% of school children get their first choice school, you come to realise that too much is being made of this issue in the press.
With maternity services, 25% of all children born in the UK have are born to non UK national mothers, about half of these are born to UK fathers. The difference between the number of children born to UK mothers and Non UK is 0.4 (1.8 and 2.2 respectively). The rate of increase in births has also been noted for years.
The problems the NHS faces is the ageing population and a fall in the amount of social care available, lower levels of funding in areas that are key and then knock on to others.
Immigration is not the issue.