Labour is to table an amendment to the Queen’s Speech calling for the 1% public sector pay cap and cuts to the police and emergency services to end.
Jeremy Corbyn says the amendment, which will be voted on on Wednesday, will be a “test case” of MPs’ willingness to oppose further austerity measures.
He will say firefighters who fought the Grenfell Tower blaze “deserve” a rise after seven years of near stagnation.
The Conservatives are expected to win a vote with Democratic Unionist support.
It comes as the Labour leader prepares to face Theresa May on Wednesday in the first Prime Minister’s Questions since the election.
Mrs May has been under pressure since losing her Commons majority, while Mr Corbyn has urged Labour to remain in campaign mode, reportedly saying he could be in power within six months.
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MPs will be asked to approve the Queen’s Speech, the government’s legislative programme for the next two years, in the House of Commons on Thursday,
This will effectively amount to a vote of confidence in Mrs May’s minority government.
The Conservatives’ deal with the Democratic Unionists – which will see the Northern Ireland party’s 10 MPs line up behind the government in key votes – gives them a working majority of 13 and means they are in little danger of losing.
But Mr Corbyn will seek to increase pressure on the government by forcing a separate vote on Wednesday on the issue of continued austerity – about which some Tory MPs have expressed concerns.
He will say public sector workers have been “denied” a pay rise for seven years and this “must change”.
Labour’s amendment praises the response of the emergency services to the deadly fire in the west London tower block, which killed at least 79 people, as well as to the terror attacks in London and Manchester.
But it calls on the government to recruit more police officers and firefighters and to give the emergency services and other public sector workers a “fair pay rise”.
Pay rises for five million public sector workers have effectively been capped at 1% since 2013, before which there was a two-year freeze on pay for all but the lowest-paid workers.
In their manifesto, Labour pledged to lift the pay cap but said it would be up to the public sector pay review bodies to decide what level of increase was appropriate and financially sustainable.
Mr Corbyn rejected suggestions he was trying to make political capital out of the Grenfell fire, pointing out that the party had called for higher pay and an end to cuts before the disaster.
“I would have thought the Grenfell fire has concentrated the minds of a lot of people on the wonderful work done by the police, fire and ambulance services,” he said.
There was a clear sense, he added, of the “way in which they are stretched and the trauma with which all workers in those services go through – we think they need more money to be paid into those services and more staff in them”.
During a debate on health, care and security, Labour will also demand a commitment from the government that it will not cut police or fire service personnel numbers in the current Parliament.
The opposition, which focused much of its election campaign on the fall in police numbers since 2010, says it would hire 10,000 new police officers and 3,000 firefighters.
It has claimed fire and rescue budgets were cut by 30% between 2010 and 2015, and a further 20% cuts are envisaged between 2015 and 2020.
“You can’t have safety and security on the cheap,” Mr Corbyn added. “It is plain to see seven years of cuts to our emergency services has made us less safe.”
The Conservatives went into the election pledging to maintain the public sector pay cap until 2020, but some MPs are now calling for a rethink after the party lost its majority.
Chancellor Philip Hammond has acknowledged that many people are “weary” after years of pay restraint and falls in their real-terms incomes.
He has pushed back his predecessor George Osborne’s target for eliminating the deficit to 2025.
But he has insisted that the Conservatives need to continue to make the case for sound public finances as the basis for increased spending on the NHS, police and other services.
A Conservative spokesman said the country was “indebted” to the heroism of the police and emergency services, but Labour’s proposed tax rises and higher borrowing would threaten investment in them.
“The truth is you can’t fund your emergency services without a growing, healthy economy – which only Conservatives in government will deliver,” he said.
“That’s why we have put forward a Queen’s Speech that will build a stronger economy so we can improve people’s living standards and fund public services.”