Unions representing 1.6 million local government workers in schools and councils have submitted a 5% pay claim, saying they want to narrow the gap between declining wages and the rising cost of living.
Employers are also being urged to move the lowest paid staff on to the voluntary Living Wage of £9.75 an hour in London and £8.45 in the rest of the country.
Unison, Unite and the GMB said the claim follows eight years of government-imposed pay restraint, which has seen wages either frozen or held to a 1% rise.
The living standards of council and school employees have "plummeted" as their pay has fallen behind inflation, the unions warned.
Unison's head of local government Heather Wakefield said: "Local government has the lowest paid workers in the public sector, and many council employees and their families are struggling to keep afloat. With every price increase, their standard of living gets worse.
"Theresa May needs to show the country she's listening to the concerns of ordinary people by coming up with the cash to give dedicated public service workers a long overdue, decent pay rise."
Unite national officer Fiona Farmer said: "Local government workers in waste, refuse, maintenance, schools and leisure have suffered from years of austerity with significant cuts to services, jobs and pay."
Rehana Azam of the GMB said: "Local government workers are suffering the worst squeeze on their pay in living memory, contributing to a public sector recruitment and retention crisis that is undermining the quality of services for everyone.
"Last week's election result was a clear vote for a new approach and against the running down of public services."
Employers spokeswoman Sian Timoney said: "We will be consulting with councils in the coming weeks on pay across the workforce and in particular how we can meet the challenge of the Government's proposed level of the National Living Wage over the next few years. The unions' claim will form part of the consultation.
"We recognise that public sector workers have had lower than average pay awards for a few years now, but local government continues to face significant financial challenges so we are surprised that the unions are seeking such an ambitious pay award.
"Local government has lost more than half a million jobs in recent years and meeting this claim would result in many more such job losses."
Meeting the claim in full would cost £559 million in 2018/19, said council employers.