Jeremy Corbyn is challenging the Conservatives to back his call for more funding for the police and fire service and for the 1% public sector cap to end.
Labour has tabled an amendment to the Queen’s Speech, which will be voted on on Wednesday.
The Labour leader said the first Commons vote of the new Parliament will be a test case for MPs’ approach to austerity.
The amendment calls for an end to cuts to police and fire services, commends their response to recent terror attacks and the Grenfell Tower disaster, backs more recruitment and calls for the public sector pay cap to be lifted.
Speaking to Sky News, Mr Corbyn said: Cuts in local government expenditure have a price to pay.
There is a link between cuts in local authority expenditure and the level of building control, inspections that have taken place and therefore the safety of the residents in those towers.
We cannot have our citizens living in danger of a fireball.
Mr Corbyn added that residents living in tower blocks had concerns over their safety and that any building which has failed a fire safety test must have its cladding removed as quickly as possible.
It is unlikely the Conservatives will back any attempt to amend the Queen’s Speech.
But Mr 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.
Chancellor Philip Hammond has suggested the Government could ease austerity measures, claiming the Tories were not deaf to the message from the General Election, where the party lost its majority.
Janet Davies, general secretary of the Royal College of Nursing, said: Hours after nursing staff have staged protests in 30 towns across the UK, MPs will have the first opportunity to show they are listening.
The protests will have left Theresa May in little doubt over nurses’ fears for the safety of their patients and why this cap on pay must go.
The Fire Brigades Union said the Government should back the amendment if it is serious about addressing all aspects of the Grenfell Tower disaster.
Matt Wrack, FBU general secretary, said: Cuts mean that fire engines are increasingly sent out without a full complement of firefighters.
This under-staffing prevents firefighters from adopting the best professional practices and procedures and will contribute to deaths that are avoidable.
A Conservative spokesman said: We’ve protected the police budget since 2015 while Labour wanted to cut it by 10% 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.