“It is conceivable that there is no majority position for any deal in the current arrangements in Parliament,” said the senior MP.
His comment was echoed privately by a former senior member of the Remain campaign team who recalled a situation when Parliament voted five times on rival proposals to reform the House of Lords, rejecting them all.
Mr Watson told the Today programme he thought another referendum was “highly unlikely” but the option had to be left in case none of the Brexit options secured a majority in the House.
“I have said many times it’s highly unlikely we will support a people’s vote, and we have not called for it, we haven’t taken that off the table because there are a rare set of circumstances where Parliament just can’t make a decision on it, and in those circumstances you’d keep your options open.”
The former Remain campaigner, a Tory grandee, said the prospect was becoming more likely as the autumn deadline approached to agree a deal capable of being passed by Parliament and agreed in the EU.
“A majority of MPs wanted reform of the House of Lords but they could not support any of the plans out to a vote,” he said. “The result was that no reform was possible. It may be that a second referendum will be the only thing that can break a deadlock and get a decision one way or another.”
A possible way forward, he said, could be a binary decision between agreeing the deal reached in talks with the EU in autumn and an option to remain in the EU under the UK’s current terms.