Ditch EU for change, Corbyn supporters stick to Brexit script

* Opposition Labour to vote on second referendum on Tuesday

* Party divided, like government, over how to leave EU

* Activist says Labour could be more radical outside bloc

By Elizabeth Piper

LIVERPOOL, England, Sept 24 (Reuters) - On a cold autumn night, trade union activist Paula Barker made a passionate plea to fellow members of Britain's Labour Party to be positive about leaving the European Union and make way for leader Jeremy Corbyn's radical new agenda.

The response - a mixture of cheers and competing calls to "stop Brexit" - cut to the heart of the main opposition party's struggle to find united ground to try to challenge the Conservative government's strategy to leave the EU.

Split, like much of the country, over how to leave -- Britain's biggest policy shift in more than 40 years -- Labour's leadership is wary of making commitments to the growing number of members who are fighting Brexit because it fears it could lose voters optimistic about a future outside the bloc.

Barker's words on the eve of the party's annual conference in the northern port city of Liverpool echoed long after the meeting began, when Labour tried to keep both sides of its Brexit divide onside by keeping a possible second referendum on the table.

That may well win favour with well-heeled London-based members of the party, who overwhelmingly voted to stay in the bloc. But for those, especially outside the capital, who voted to leave in frustration at a system they say is stacked against them, Brexit offers opportunity.

"Labour needs to be a party of popular mobilisation and radical change. We need to be very wary of being labelled as a middle-class pro-Remain or pro-EU party," Barker shouted at hundreds of Labour supporters amassed on Liverpool's pier head on Saturday evening to see Corbyn take the stage.

"It would be disastrous for Labour to say 'No, we know best - you may have little or nothing to lose but stick with the status quo' ... We should remember that a radical Labour government outside the EU and the single market would be better able to implement its radical economic programme."

It is an argument Labour's leadership feels keenly, and one that almost certainly chimes with Corbyn, a veteran eurosceptic who in 1975 voted "No" to Britain's membership of the then-European Community.

Corbyn has long been more interested in ending austerity in Britain and launching an economic programme to reverse cuts he says have hurt the poor for the benefit of the "super rich".

Outside the EU's state aid rules, he could renationalise Britain's mail, rail and utilities. Free of the bloc's competition directives and procurement rules, Labour could protect and expand the public provision of public services.