Allie Renison, the head of Europe and Trade Policy at the IoD, also said that Brexit could provide the UK with an opportunity to deepen trade ties with Commonwealth countries.
Ms Renison argued that in order for the UK to exit in a “smooth and orderly way” the country must not give the impression that it was trying to drag out the process, or not leave the EU at all.
The IoD has called on the Government to immediately guarantee that the three million EU citizens who are resident in Britain will be able to live here after we leave the European Union, in order to reduce uncertainty for employers and employees.
Ms Renison said: “Just under 40 per cent of our members employ EU nationals. You’d be surprised about the amount of nervousness that is genuinely giving to a lot of these employees.”
She said it appeared that, both from the EU and UK side, “they are willing to talk about that right away to give people those assurances”.
Speaking during a trip to Leeds, Ms Renison said that there were a lot of countries who were excited about the UK trying to expand its trade focus.
She added: “It focuses minds...on the rest of the world. We had this meeting of Commonwealth trade ministers in London a few weeks ago.
“We have to be, in one sense, realistic about the fact that we don’t have imperial dominance anymore.
“We can’t force these countries to be interested in us. And yet, a lot of them are; they see Brexit as an opportunity to try and deepen some of those ties.
“There were quite a few countries in the Commonwealth that felt a little bit aggrieved when the UK entered the European Economic Community because it completely changed their trade relationship.
“Brexit is becoming a hook for both the UK and the rest of the world to start looking at each other with a more targeted focus.”
In order to reduce economic uncertainty, the IoD has asked for a commitment from politicians on all sides to rule out a second referendum on EU membership in the next Parliament.
Ms Renison said: “In order to make sure that we exit the right way, in a smooth, and orderly and clean way, we need to make sure that people don’t think that we’re trying to drag on the process or not leave.
“That’s why, one of the things we are calling for politicians on all sides to say is, ‘No, we’re not going to have another referendum. We are committed to carrying out Brexit, to try and give people confidence that this is not about trying to hang on to the EU itself in any way.
“It’s making sure that you don’t have a disorderly exit and that there is no potential uncertain legal vacuum in between.”
Another area of contention could be the size of the UK’s “divorce bill” from the EU.
EU chiefs are expected to seek an early agreement on an exit fee - meant to cover the UK’s outstanding liabilities such as pensions and projects.
European Commission president Jean-Claude Juncker has confirmed that he expects the UK’s divorce bill for Brexit to be around £50bn.
Brexit Secretary David Davis has said the UK would meet its obligations - but he did not expect to see “that sort of money change hands”.
Ms Renison said: “On the bills with respect to what our liabilities are, that’s something thankfully, that business doesn’t have to worry about.
“But the reason that it could become a worry, is if this becomes an argument right at the start and becomes one that is insurmountable, and it basically drives both sides to say, ‘Well, if we can’t agree, we just won’t have a deal.’
“That’s where there would be the most concern.
“Interestingly, when it comes to money generally, this is one of the arguments for saying, ‘You can’t completely separate out withdrawal from new framework because we are going to keep contributing to the EU budget for programmes that we want to be part of.
“The way that the EU does its budget payments it will be quite hard to completely set apart what we need to pay as part of leaving from what we will pay going forward - they are interlinked in so many areas.
“The UK will be able to use that argument to say, ‘We will talk about the potential for a divorce bill, so to speak, but we have to talk about it in a wider framework, about what our financial obligations are going forward.”
A Government spokesman said: “The Prime Minister has been clear that we will be seeking an early agreement on the rights of UK nationals in the EU and EU nationals in the UK, on a reciprocal basis.
“This is a priority issue for the forthcoming negotiations. Over the last nine months the Government has also been engaging directly with businesses up and down the country to build a strong understanding of the challenges and opportunities that our EU exit brings.”