In an interview with The Guardian Jon Trickett, MP for Hemsworth, said: “There are a large number of people in my constituency who remain attached to the idea that we ought to leave.
“I think if Labour is to attach ourselves to the idea of a second referendum, we have to offer them an opportunity of voting for a Labour Brexit.”
Jeremy Corbyn has committed to holding a People’s Vote within six months in he were to become Prime Minister, but the party fell short of backing remain at its annual conference, where members instead voted to take a neutral position in any campaigning.
Labour may try to attach the condition of a second referendum onto Boris Johnson’s Brexit deal, if one is agreed and brought before Parliament in a special sitting on Saturday.
But Mr Trickett - whose view mirrors Mr Corbyn’s - said the preferred course was to vote dwn a Tory deal and then remove the Government.
“I think that is the order in which things should be done,” he said.
But he said in Hemsworth “Brexit isn’t mentioned that much”.
He said: “People who are very, very impassioned by Brexit will talk about nothing else. But the vast majority of people are talking about bus services, cuts to the health service, the cost of living.”