The chances of Britain leaving the European Union are less than 1%, according to an Ipsos MORI poll.
The poll found 48% of those questioned in the UK want Britain to remain within the bloc, while 40% want to leave it and 4% would like to stay.
But a slim majority of those polled said they thought the country would remain in the bloc.
It is the first poll in the aftermath of last month’s Brexit vote that has shown a clear majority of voters support remaining in the European Economic Area, or EU.
But Mr Corbyn has said he would not seek to bring the UK back into the EU without a deal.
Labour leader Jeremy Corbyn says he will not seek a second referendum, but will not quit the EU after Brexit.
Theresa May is expected to announce her government’s position at a cabinet meeting on Monday.
Mr Corbyn has already said he wants to negotiate a deal with the EU that will allow the UK to leave without a second Brexit vote, if needed.