London (CNN) -- Dozens of alleged sexual abuse victims of the late BBC entertainer Jimmy Savile are suing both the British broadcaster and Savile's estate, a lawyer said Wednesday.
A recent police investigation, conducted after Savile's death, suggested that the DJ and children's entertainer could be among the most prolific abusers in the country's history.
Some of alleged sexual assaults occurred on BBC premises, police said.
Alan Collins, of the law firm Pannone, said it had prepared 31 cases so far against Savile's estate "and others including the BBC."
"The purpose of issuing the writ is to protect our clients' position and to seek management directions from the court to ensure the claims are administered as efficiently as possible," Collins said in a prepared statement.
The attorney said he could not comment in detail about the nature of the cases or the allegations, but said they "range in seriousness from inappropriate behavior to serious sexual abuse."
An anonymity order has been put in place "given the highly sensitive nature of the case," the law firm said.
A BBC press office statement said the company was "unable to comment on any legal claims of this nature made against the corporation."
Another law firm, Gordon and Slater, told CNN it is representing more than 60 alleged Savile victims but has not as yet started court proceedings.
The potential defendants are the BBC, the Savile estate and a number of hospitals.
"We are in meaningful discussions with all the potential defendants, including the Savile estate," said lead lawyer, Liz Dux.
"We do not believe the commencement of litigation at this stage to be either necessary or in our clients' best interests. Should that position change, we will take action immediately."
The police probe began after a TV documentary broadcast in October sparked a flood of sexual abuse claims against Savile.
Three months later, police unveiled a report exposing "vast, predatory and opportunistic" abuses by Savile across a span of half a century, involving some 450 victims.
Nearly three-quarters of his victims were children, the January 11 report said, with the youngest only 8 years old. Most, but not all, were female.
The earliest claim against Savile, who was still a household name when he died in 2011, dates from 1955 and the latest from 2009, when he was in his 80s.
Savile used his celebrity to "hide in plain sight" as he opportunistically preyed on the children and young people with whom he came into contact as he presented BBC children's show "Jim'll Fix It" and music show "Top of the Pops," the report said.
A BBC statement issued when the report came out said it was shocked by the revelations.
"As we have made clear, the BBC is appalled that some of the offenses were committed on its premises. We would like to restate our sincere apology to the victims of these crimes."
The broadcaster has set up its own inquiry looking at whether the culture and practices within the BBC at the time enabled Savile to abuse children. More than 350 people had contacted the inquiry team as of Monday.