“Only Labour has been consistently trying to find a way through the deadlock,” Mr Corbyn is expected to say.
“We don’t believe the real divide in society is between people who voted to remain or to leave the European Union.
“We believe the real divide is between the many – who do the work, create the wealth and pay their taxes – and the few – who set the rules, reap the rewards and dodge their taxes.”
In his conference speech Mr Drakeford told delegates that Theresa May was the “first Prime Minister in history to fall on her own sword – and then to miss it”.
The Welsh Labour leader accused the Conservative party of being “wrapped and trapped by a mythical nostalgia for a past remembered only by its ever diminishing membership”.
He said “the chaos of Brexit” is seen as an opportunity for Mr Cairns “to grow his own office”.
“So let me issue this very clear warning to the Secretary of State for Wales,” Mr Drakeford said.
“If he continues to persist in using the ‘so called’ UK Shared Prosperity Fund as a means of by-passing the National Assembly, as a way of using Brexit to short-change the people of Wales, then he is heading for a fight,” he said.
The FM said EU funds must be replaced, and devolved powers kept: “Not a penny less, not a power loss”.
And he said he had a “simple message” to voters and Labour members on the European elections, saying they should be taken as seriously as a general election.
“You will be told that these elections are meaningless; that it’s not worth bothering to turn out to campaign or not even bothering to vote,” he said.
“Please do not believe it.”
New MP Ruth Jones, who won the by-election last week, gave the welcome address at conference, telling delegates that in devolution’s 20th year “our task is to stand up for the people of Wales”.
“People have had enough after a decade of austerity,” she said, calling it a “political choice, not a financial one”.
Shadow Welsh Secretary Christina Rees appealed “for calmness in a country that is divided because of the inexplicable way the prime minister has handled the Brexit negotiations”.
She said language in emails and on social media had become “intimidating”, and had reported the worst cases to the police.
“It’s changed from ‘I’m writing to tell you I don’t agree with you’ to ‘You’re a traitor, letting down people who voted for you’,” she said.