The challenge comes after the authority set its new budget for the year - resulting in a 2.99 per cent rise in council tax.
At its budget meeting last week, councillors voted to pass an amended version of the initial budget which had been tabled by the ruling Conservative party.
A proposal of no confidence in the executive cabinet and a motion to remove the leader of the council with immediate effect has been put forward by councillor Paul Foster, leader of the opposition.
In an official statement he said: “We can confirm we have formally submitted a no confidence motion to remove the leader and cabinet once and for all from any position of responsibility at South Ribble.
“The performance of the executive is at best chaotic, at worse inept. They continue to ignore critical advice of Officers, make no attempt to discuss issues impacting on the entire borough, and most critically, continue to fail to get policy supported at council.
“In losing their budget vote it was the final straw, losing what little credibility they had left.
“What is worse, they know their wholly inappropriate leadership is having a hugely detrimental impact on the residents we are elected to serve, but this is of no concern as long as they retain absolute power.”
The council said correct procedures were followed at the budget meeting.
Meanwhile independent, councillor Paul Wharton is calling on central government to intervene as he says he believes the way the new budget was passed is open to legal challenge.
Councillor Peter Mullineaux, council leader, said: “This year we are announcing much more than an annual budget for South Ribble – we are announcing our vision for the future, and a five-year plan of how we will get there. We want South Ribble to be a place with high employment, good schools, with access to affordable homes, high life expectancy, and a place where people feel safe.”
For householders, the council tax rise will mean an increase of £6.23 a year – for an average Band D property.
The £13m annual budget underpins the council’s new a five-year plan detailing plans for the area and how the council will deliver them.
Over the next five years, the council will invest more than £42m in improving services for residents and transforming the way the council works.