60 per cent of those who expressed a view were in favour of remaining in the single market, according to the BMG Research poll for the website Left Foot Forward.
24 per cent neither agreed nor disagreed and 16 per cent wanted to leave.
57 per cent said the UK should remain a member of the customs union, while 27 per cent neither agreed nor disagreed and 16 per cent backed leaving it.
BREXIT LATEST – MORE ANALYSIS FROM YAHOO UK:
Article 49: What is it and how can it reverse Brexit after the UK leaves the EU?
How the ‘Brussels Effect’ will continue to run Britain’s economy long after Brexit
How will Brexit affect your finances in 2018?
Facebook widens probe into Russian influence on Brexit vote
Second vote not undemocratic, Irish PM says on Brexit
The survey was carried out before French President Emmanuel Macron warned that a post-Brexit free trade agreement would not provide full access to the single market for financial services at the same level as that offered to members.
Speaking alongside Theresa May after a UK-France summit on Thursday he said: “I want to make sure that the single market is preserved because that is very much the heart of the EU.
“The choice is on the British side, not on my side. But there can be no differentiated access for the financial services.
“If you want access to the single market – including the financial services – be my guest. But it means that you need to contribute to the budget and acknowledge European jurisdiction.
“Such are the rules, and we know the system already in place for Norway.”
The Prime Minister plans for the UK to leave the single market and customs union but strike a bespoke deal which will preserve many of the benefits.
“We recognise that as we leave the EU we will no longer be full members of the single market,” she said.
“There will be a different relationship in future, a different balance of rights and responsibilities, and we’ve been very clear about that.
“But I believe that it is actually in the interest not only of the United Kingdom, but also the European Union as it goes forward, to continue to have a good economic relationship and partnership with the UK and I believe that should cover both goods and services.”