A survey of 2,765 members of the Institution of Mechanical Engineers (IME) found 56 per cent support staying in the EU, compared with 27 per cent who want to leave. Some 17 per cent are undecided.
However, the figures compare to a similar survey in 2015 which found 72 per cent supported the UK's continued EU membership, with 24 per cent wanting to leave.
Stephen Tetlow, chief executive of the IME, said respondents felt the main benefit to the UK’s membership in the EU is better access to markets (46 per cent), while about 60 per cent of the engineers surveyed said that bureaucracy imposed by the EU was detrimental to UK manufacturing and engineering.
Some 49 per cent said leaving the EU would make the UK less attractive as a European base for global manufacturers, while a third said they were concerned over the potential of trade barriers being erected if the UK does vote for Brexit.
"Whatever the outcome of the referendum in June, the government needs to ensure the result does not damage the UK’s vital engineering and manufacturing sectors," Tetlow said.
"The government must focus on the key engineering issues likely to be affected by the decision. The most pressing are improving access to markets and people with the right skills, ensuring open access to foreign investment and growth in research funding as well as ensuring the UK is still able to continue to play a leading role in influencing European codes and standards."
The poll also found that 64 per cent of engineers surveyed feel that uncertainty over the UK's role in Europe was having a negative effect on manufacturing.
Earlier this month the Office for National Statistics released figures showing industrial production decreased by 0.4 per cent during the first three months of the year, with manufacturing - the largest component of the category - also down by 0.4 per cent.
The news from the IME comes the day after an ORB poll for the Telegraph which found increasing support for the Leave campaign.
The poll found that the lead for Remain had been reduced to just five points, down from 13 last week.