The Kantar poll of 1,172 people found that 51% of Britons would like a referendum to be held on the deal once negotiations between the Government and the EU have come to an end.
One in three - 32% - would not like a public referendum to be held, and the remaining 17% do not know.
Support for a referendum on the deal includes 35% of people who voted Leave in the 2016 referendum and 67% of people who voted Remain.
The poll also put Labour three points ahead of the Conservative Party on voting intention.
Some 35% of the public would vote for Labour, the poll found, while 32% would vote Conservative.
The poll shows a nine-point drop in support for the Conservative Party compared to the same poll last month, and a four-point gain for Labour.
The Liberal Democrats polled at 11%, Ukip at 7%, the SNP at 5%, the Green Party at 4% and Plaid Cymru at 1%.