The first vote of the new Parliament will see MPs decide whether to lift the public sector pay cap on emergency service workers.
Labour has tabled an amendment to the Queen’s Speech - which the Lib Dems will back - to attempt to force the government to end austerity and give the police force and fire service a pay rise.
It comes as research by the party reveals the Tories’ proposed ‘sweetheart deal’ with the Democratic Unionist Party (DUP) - in which the prime minister agreed to spend an extra £1bn on Northern Ireland over the next two years for infrastructure including health and education - means the rest of the UK will lose out.
Labour says House of Commons Library figures suggests that if the deal goes ahead and rises to £2bn as some reports suggest, it could mean £68bn in government funding is denied to the rest of the country.
Under the Barnett Formula - the system which sets public spending for devolved governments - an increase of £2bn for Northern Ireland would normally imply additional public expenditure in England of £59bn, with Scotland getting an extra £6bn and Wales £3bn.
But the Conservatives have decided not to increase funding across the board and have not yet revealed how the increase in spending for Northern Ireland will be funded.
Shadow Chancellor John McDonnell said: “We need to see an end to austerity throughout the UK not just in Northern Ireland, and not just to prop up Theresa May and her failed government.
“Labour’s fully costed alternative programme of government stands ready to provide Britain with the leadership that will truly end austerity, and unite all nations and regions in our country.”
Labour’s Queen’s Speech amendment, which will be voted on on Wednesday evening, says the efforts of the emergency services during the recent terror attacks and Grenfell disaster should be acknowledged.
Leader Jeremy Corbyn said: “You can’t have safety and security on the cheap. It is plain to see that seven years of cuts to our emergency services has made us less safe; it’s time to make a change.
“Our emergency service workers make us proud at the worst of times for our country and deserve the pay rise they have been denied for seven years.”
Ahead of the vote, Corbyn will face Theresa May for the first Prime Minister’s Questions of the new Parliament, at which he is expected to raise cuts to police and fire services.
A Conservative spokesman said: “We are all indebted to our emergency services and their heroic responses to recent terror attacks, the bravery seen at Grenfell Tower, and the work every day that has seen crime cut by a third.
“We’ve protected the police budget since 2015 while Labour wanted to cut it by 10 per cent - and the number of fire incidents has halved in the last decade. We have also given the police and intelligence agencies given the powers they need to respond to increased threats and keep people safe.
“But the truth is you can’t fund your emergency services without a growing, healthy economy which only Conservatives in government will deliver – 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.”