Wendy Nichols, a member of Labour's ruling national executive committee who chaired the Monday morning debate at the party's conference in Liverpool, appealed for delegates not to boo when the results were announced, after heckling emerged following a separate vote on Sunday.
Opponents say this is part of an effort to purge "Blairites" and other critics of leader Jeremy Corbyn from the party, while supporters of the change say it will help a new generation of Labour MPs emerge.
Shadow chancellor John McDonnell said the "real people's vote" would be a general election and said that if there was another referendum there should not be the option to remain.
Labour is expected to discuss several motions on Brexit at its conference, and it remains unclear what the proposal on a second referendum might be - it could be a clear backing of a vote or something less black-and-white.
'Jeremy Corbyn promised a radical expansion of democracy in the economy and wider society and this logic must extend to the Labour Party too.
Labour MPs campaigning for a so-called people's...
Corbyn has long said that a "People's Vote" is not off the table for his party, and a source close to the leadership urged caution over an as-yet unknown motion, repeating the Labour leader's stance that he does not support a second referendum.
He added: 'But I was elected to empower the members of the party.
Many within the party support mandatory open selection contests for all MPs ahead of every election.
The country's path out of the bloc is even more unclear after weeks of positive noises about the prospects of clinching a divorce deal and one on a future trading relationship, the mood between Britain and the European Union turned sour on Thursday. He told the Sunday Mirror newspaper "I'm not calling for a second referendum".
Mr Watson told The Observer: "Jeremy and I were elected in 2015 to give the Labour Party back to its members".
"In that case it will be about whether you accept the deal or not or whether you send people back to negotiate a proper deal".
Andrew Adonis introduced at People's Vote rally as "the politician who went from Bambi to Rambo".
"My big worry is that if we go for a referendum which is seen as just a simple re-run we could divide the country again, we could get nearly the same result or if it's slightly different than people demand another referendum".
The rule change for future leadership contests does not alter the 10% threshold for the number of MPs' nominations which a candidate must gather to get on to the ballot paper, but also requires would-be leaders to secure nominations from 5% of constituency parties or 5% of members of trade unions or affiliated organisations.