The British Chambers of Commerce (BCC) found 54.1 per cent of more than 2,200 members who completed the survey said they would vote to remain in the EU and 37 per cent said they were backing an exit.
Support for Remain was down seven points from 60 per cent in February, while Brexit support was up from 30 per cent.
Nearly nine in 10 of those surveyed said they are unlikely to change their mind before the 23 June vote.
The survey also found the majority of those surveyed reported no impact to date on their business as a result of the referendum.
If the UK were to vote to leave the EU, 35.9 per cent said they would expect this to have a negative effect on their overall growth strategy – down from 39 per cent in February. Some 36.3 per cent said it would have no impact and 15.9 per cent said it would be positive.
On the impact on overall growth strategy of staying in the EU, 12.8 per cent said it would be negative, 49.4 per cent thought it would have no effect and 30.1 per cent believe it would be positive.
Dr Adam Marshall, BCC acting director general, said: “While only a minority of businesspeople report that the referendum campaign has had a material impact on their firms to date, much larger numbers say they expect significant impacts in the aftermath of the vote.
“Whichever outcome prevails, Westminster must shift its attention back to the economy on June 24 without delay. Growth is softening, and Westminster’s referendum ‘tunnel vision’ over the past year has meant that far too many key economic issues have been given short shrift or delayed altogether.”
Read more: Ready for a Brexit? Most firms are not
In response to the survey, Vote Leave chairman John Longworth said: “Despite the claims of the pro-EU camp to the contrary, business is not fearful of the referendum or the result. This is because they know it is safer to take back control and spend our money on our priorities.”
Will Straw, Britain Stronger in Europe's executive director, said: “Walking away would be a leap in the dark. So it’s unsurprising that today's poll confirms that British business is adamant that we must stay in the EU.”