A third of the manufacturers surveyed said that their business needs cannot be found among UK nationals, while others say they recruit EU nationals because they have a better work ethic, have foreign language skills, or because they are part of an intra-company transfer programme, the EEF said.
On average, EU nationals make up 11% of the manufacturing workforce, UK nationals 87% and non-EU nationals the remaining 2%, it said.
Larger firms are more likely to recruit EU nationals than smaller firms. Just under half (48%) of the smallest companies had no EU nationals.
The EEF also reported a geographical variation with EU nationals more likely to work in Greater London, the South East and the East Midlands, and less likely to work in the North East, Scotland and Wales.
The impact from the Brexit vote has been limited to date, with only 16% of respondents saying they have seen an increasing number of EU nationals leaving their business. However, 26% have seen a decrease in applications from EU nationals, the EEF said.
It will be "significantly damaging" if Brexit involves applying the same restrictions to EU nationals as to non-EU workers. Salary thresholds and time restrictions on how long EU nationals can stay in the UK would also create problems.
The reciprocal rights of EU nationals in the UK, and UK workers in the EU, must be clarified, the EEF said.
Prime minister Theresa May has proposed a new 'UK settled status' for EU citizens already living in the UK, if a similar deal can be reached with the EU for UK citizens abroad.
The EEF has also called on the government to allow industry to continue to recruit low-skilled EU workers until the UK labour market is able to meet demand, and to allow skilled workers from the EU to work for up to five years and then apply for permanent residency.
Global companies should be allowed to recruit and move employees through intra-company programmes and post employees to and from EU countries, while EU students should be encouraged to study in the UK and be allowed to seek work after they finish their studies, the EEF said.