Labour should be prepared to back demands for a new Brexit referendum, deputy leader Tom Watson has said.
He told the Observer he would prefer Brexit to be debated in an election but if members favour another public vote, their views must be respected.
A poll for the paper suggests 86% of members want a final say on the UK's future relationship with Europe.
Mr Watson said there could be "pressure" to commit to another Brexit vote in its next election manifesto.
The party has never formally rejected the option of second vote but leader Jeremy Corbyn has indicated he would prefer the issues to be resolved in an election.
He is expected to face pressure at the party's annual conference in Liverpool to commit to a new referendum.
MPs and union leaders are set to join a march on the conference's opening day on Sunday calling for what campaigners have called a People's Vote.
The YouGov survey of 1,054 Labour members, commissioned by the People's Vote campaign, found 86% supported a referendum on the outcome of Brexit negotiations, against 8% who oppose it.
In his interview with the Observer, Mr Watson said: "Jeremy and I were elected in 2015 to give the Labour party back to its members.
"So if the people's party decide they want the people to have a final say on the deal, we have to respect the view of our members and we will go out and argue for it."
It came as Labour's ruling National Executive Committee agreed changes to the party's rules to give grassroots activists and trade unions more say in who can stand in future leadership elections.
The NEC, meeting in Liverpool, also agreed reforms to make it easier to deselect sitting MPs and backed the creation of a second deputy leadership post.
By Iain Watson, BBC political correspondent
Two significant shifts have happened on the eve of Labour conference and they both involve Tom Watson.
While not technically departing from the party's official line that a new Brexit referendum shouldn't be "off the table" but an election is preferable, the deputy leader is sounding far warmer to the referendum idea after a poll of Labour members suggested 86% would back one.
He has suggested that if there were an early election then there would be pressure to make a referendum a manifesto commitment.
His views are important because - like Jeremy Corbyn - he has a mandate from the membership.
But another development should not be understated.
Labour's National Executive has decided to recommend the creation of an additional deputy leadership post.
That raises the prospect of a candidate standing on a platform of new EU referendum. If they get that mandate, the pressure on the existing leadership to change position could reach boiling point.
Theresa May's plan for Brexit - known as the Chequers agreement - was rejected by EU leaders as unworkable at a summit in Salzburg on Thursday.
The prime minister later said the EU's rejection of her plan without offering an alternative was "unacceptable" and made it clear she was ready to walk away from the negotiations rather than accept a "bad deal".