Jeremy Corbyn is to address union leaders and members in his first policy speech since becoming Labour leader.
Mr Corbyn, whose anti-austerity message won him the backing of major unions, will appear at the TUC annual congress.
He finalised his shadow cabinet on Monday but faced tough questions from his MPs on the make-up of his team and his stance on Europe and other issues.
He is also due to attend a service to mark the anniversary of the Battle of Britain.
Mr Corbyn has sought to address some of the ructions caused by his victory by forming what he said was a “unifying” shadow cabinet but his appointment of fellow left-wing MP John McDonnell to the key role of shadow chancellor has angered some in the party.
Some MPs have also expressed concern about his position on Europe amid uncertainty about whether he would countenance campaigning to leave the European Union in a referendum due to happen before 2017.
At a meeting of Labour MPs on Monday, Mr Corbyn said Mr Cameron must not be given a “blank cheque” in his negotiations with other European leaders and the changes he agreed to social and employment protections had to be “right ones”.
Only a small proportion of MPs backed Mr Corbyn to be leader and while the BBC’s Norman Smith said there was no outright anger shown towards him, he had faced searching questions on Europe, Syria, Trident and the economy.
Mr Corbyn has pledged to oppose the government’s spending and welfare cuts and also to challenge a proposed new law tightening the rules on trade union strike ballots. Proposals that would impose a 50% threshold for participation in strike ballot, and a 40% threshold for stoppages involving essential public services, passed their first parliamentary hurdle when they were backed by MPs by 33 votes.
Among other key appointments made by Mr Corbyn, Angela Eagle was named shadow business secretary and shadow first secretary of state, and her twin sister Maria defence secretary. But more than 10 former shadow ministers have refused to serve under him.
Speaking on BBC Two’s Newsnight programme, Angela Eagle said Labour always had a “democratic policy making process” but Mr Corbyn wanted to encourage more debate within the shadow cabinet.
She said that would lead to a “reset of the way we do things” amid concerns a “dictatorial, strong man, ‘what I say is somehow party policy'” approach had been adopted in the past.
Ms Eagle said campaigning to remain in Europe “has got to be the aim but we are not going to, before we even know what the prime minister is going to come back with, know precisely how we are going to be campaigning”.
‘No celebration’
In his first TV interview on Monday, Mr McDonnell said capitalism was “failing” and he wanted to “transform it”. He told Channel 4 News he believed the role of shadow chancellor was “to put forward an alternative to what’s happening at the moment”.
He said he was “not particularly interested in tax on income” and instead wanted to focus on those who were “literally laughing all the way to the bank” and “not paying their fair share”.
Writing in the Times, Chancellor George Osborne said that Mr McDonnell’s appointment broke decades of economic consensus.
“Far from celebrating this turmoil, for me, as chancellor, this means going back to first principles and winning again the arguments made by both Conservative and previous Labour governments alike,” he said.
“As the whole Labour party shifts left, abandoning the centre ground, it abandons the working people of this country, including millions who voted Labour but do not support the ideas of the party’s new leadership,” added Mr Osborne.
