* Opposition Labour to vote on second referendum on Tuesday
* Party says new national election best solution to impasse
* Leaders say new referendum would not be on staying in EU
* PM May has ruled out a second referendum (Adds Labour Leave comment, People's Vote)
By Elizabeth Piper and Kylie MacLellan
LIVERPOOL, England, Sept 24 (Reuters) - Britain's opposition Labour Party will vote this week to keep a second Brexit referendum as an option if Theresa May fails to pass her plan to quit the European Union through parliament, heaping pressure on a struggling prime minister.
But with the leadership intent on any such referendum not allowing a re-run of a 2016 vote to stay or leave the EU, the move could reignite tensions in the party, which, like much of Britain, is divided over how to quit the bloc.
After May's plans for Brexit - the biggest shift in British policy for more than four decades - were rebuffed by the EU on Thursday, the outcome of talks to leave are more uncertain than ever and have boosted those who want to stop the divorce.
Labour leader Jeremy Corbyn has been reluctant to support growing demands for a second referendum, or People's Vote, but the party agreed a motion after five hours that went some way to appeasing members who want another chance to vote on Brexit.
Labour agreed late on Sunday night the party would vote on Tuesday on a motion committing the party to support "all options remaining on the table, including campaigning for a public vote" if no election is triggered by May's Brexit plans.
For Corbyn's backers, the motion does little to change his position that Labour prefers a new national election to a second vote, which will ask a different question from the one posed at the 2016 referendum in which the Leave campaign beat Remain by 52 percent to 48 percent.
Corbyn's second in command, finance spokesman John McDonnell repeated that Labour was ready for an election, which he said was the "best solution", and that any new vote would not be a repeat of the 2016 referendum to stay or leave the bloc.
The Labour Party says the motion is not "prescriptive" on what the question of any second referendum should be, leaving options open to gauge the lie of the land if, or when, such a vote needs to take place.
BABYSTEPS OR BETRAYAL?
A source in the campaign for a People's Vote cautiously welcomed the move, saying: "We feel it's moved in the right direction." "It's always going to be babysteps rather than a giant leap but it's an important shift."
In the opposing corner, Brendan Chilton of Labour Leave told Reuters: "There are 5 million Labour leavers in the country who will look upon this motion with dismay."