The push for Theresa May to examine the force’s behaviour “at every level” came after acting chief constable Dawn Copley, who replaced David Crompton following the inquest findings, offered to step down.
Elkan Abrahamson, a solicitor for the victims’ families, labelled SYP a “shambles” and said there needed to be “rigorous and continuing examination” of the force’s behaviour.
He added that the force had not abided by its motto, Justice with Courage.
Mr Abrahamson, of legal firm Broudie Jackson Canter, said in a statement: “We are appalled to see the shambles in South Yorkshire Police following the Hillsborough Inquest verdict. SYP leadership have showed a lamentable refusal to face up to the fact that their organisation needs to take a long hard look at their values and ethics.”
He called for the Home Secretary to send in a team to look at the force, “root and branch, to speak to the rank and file and see what they think is wrong in the force and what needs to be done”.
Mr Abrahamson issued the statement following news that Mrs Copley’s conduct at her former employer, Greater Manchester Police, was being investigated.
GMP confirmed “an independent investigation was undertaken by Kent Police following a number of allegations”.
According to reports, this involved a group of senior officers who were accused of “corrupt practice”.
In the statement, Mr Abrahamson added: “We believe the rank and file officers in the force are being let down by their leaders. Sadly the only solution would appear to be the application of remedial measures and we have today asked Theresa May to commence the procedure to enable this.
“We believe there needs to be a rigorous and continuing examination of the ethical behaviour of the force at every level. The Force’s motto is ‘Justice with Courage’ - sadly they have shown neither.”
Earlier he described the force as “rudderless” when speaking on BBC Radio 4’s World At One.
He told the programme: “It is rather bizarre and it suggests that whoever is running South Yorkshire Police simply has no idea what’s going on, and the force seems to be rudderless at the moment.”
Labour’s Keith Vaz, who chairs the Home Affairs Select Committee, said the calls should be taken “seriously” and branded the force “troubled”.
“There is a short-term crisis that needs to be dealt with and it can only be dealt with by the Home Secretary,” he told the programme.
South Yorkshire’s police and crime commissioner Alan Billings said that Mrs Copley had “offered to step back to her substantive role” while another candidate was sought.
The police chief did not want “any further negative publicity or criticism to be levelled at the force”, Dr Billings added.
He said he had been made fully aware of the allegations when Mrs Copley was originally appointed as Deputy Chief Constable.
“As this matter has not yet been concluded I am unable to comment publicly on the allegations and the outcome but as soon as I am able, I will do so,” he said.
“In the meantime Mrs Copley has my full support. However, Mrs Copley has made clear to me that she does not want any further negative publicity or criticism to be levelled at the force.
“In the interests of the force and the workforce she has therefore offered to step back to her substantive role to allow me to seek support from the College of Policing in identifying another chief officer from outside the force to act as temporary chief constable until a recruitment process can take place.”
He said she would stay in post for a short amount of time to deal with pressing matters, but this would be kept as short as possible.
“I am sorry that I cannot say anything more definite at this time but we have been working closely with national bodies about these issues and hope to make a further announcement in the coming days,” he said.
It is the latest embarrassment for the force, which has been heavily criticised for its handling of the aftermath of the Hillsborough tragedy.
It emerged that the secretary of the South Yorkshire branch of the National Association of Retired Police Officers (Narpo) had posted online that officers had done a “good job” despite the deaths of the 96 fans.
Rick Naylor, whose comments have since been removed, said ex-officers acted with “dignity” despite the “bile and hatred” aimed at them.
The comments were made after an inquest jury found that all 96 victims of the Sheffield football stadium disaster were unlawfully killed and police errors contributed to the unsafe conditions.
Mr Crompton had been suspended on Wednesday amid an outcry over the handling of the inquest.
At the same time, Operation Resolve revealed that of the 100 people who refused to speak to its investigation team, 38 were police officers on the day of the disaster.
Meanwhile, Jon Stoddart, head of Operation Resolve, said investigators had no power to compel witnesses to cooperate with them.
He said some of those who have not been spoken to are believed to hold ‘significant witness evidence’.
He said: “Unfortunately, we have been unable - largely through health reasons - to interview them.”
Yesterday a police constable who was on duty during the Hillsborough disaster has said she feared senior officers would ‘throw us to the wolves’ if she spoke out.
Fiona Nicol, who was a constable when she volunteered to police the game on her day off, said she had been scared of reprisals from the police hierarchy.
She told the BBC: “I thought they were trying to blame and scapegoat us and if the opportunity had come they would throw us to the wolves.”