Josephides told the Abta Travel Matters conference in London that the UK had prospered from being inside the EU over the last few decades.
“The UK has benefited more than other member state in terms of growth through membership of the EU,” he said.
“However you decide to vote – vote with your brain and leave emotion out of it.”
With opinion polls showing that the referendum on Thursday is too close to call, speakers at the conference were not willing to make predictions about the outcome.
Deloitte’s Graham Pickett, who is lead partner – travel, hospitality and leisure, said: “There are clearly some challenges around this uncertainty and we will have massive uncertainty if we go for Brexit.
“That’s the biggest worry I have. You have already seen the devaluation of sterling over the last three or four months. This makes things a lot more expensive and that does impact on the holidaymaker.
“The currency situation could be very damaging for this industry.”
Abta’s chief executive Mark Tanzer said that the first priority for the association following a Brexit vote would be to reassure customers about this summer’s holiday plans.
“We will reassure people that nothing is going to change in the short term in terms of booking holidays for this summer – other that you might get fewer euros out of the cash machine,” he added. “The process of withdrawal will take a while.”
Abta and Deloitte produced a report looking at the impact of Brexit on the UK travel industry earlier this year.
“The conclusion for travellers and the travel industry was that we have more to lose than gain from leaving the EU,” said Tanzer.
“We have not been telling them how to vote but telling them of the potential impacts for them as travellers.”
Abta’s head of public affairs Stephen D’Alfonso added: “Apart from the economic impact, it will only be after two years that we would understand what leaving actually means and what the UK deal with the EU will be.”