Alan Collins, a solicitor at the law firm Pannone, who is representing five of Savile's alleged victims, said Her Majesty's Inspectorate of Constabulary (HMIC) should investigate why no action was taken by police.
"There should be an independent investigation into the decisions that were made," Mr Collins said.
"There are key questions about what happened to several claims made against Savile and who decided how they should be followed up.
"There are police forces who had complaints on their books and chose not, for whatever reason, to pursue matters. That is a serious concern."
At least three forces - Surrey, Sussex and Jersey - are known to have been aware of allegations against Savile, and a handful of others could also be involved.
"We need to know: did they look at their databases? Did they talk to each other?" Mr Collins told the Observer.
HMIC said: "Although we are not currently inspecting the issues around this case, we are monitoring the developments. HMIC have a programme of inspection work around child protection which is under way."
The Independent Police Complaints Commission (IPCC) is not investigating because it has received no complaints.
Mr Collins said lawyers acting for alleged victims could take action to force police forces to hand over their files on Savile.
Such action would be taken if organisations like the BBC or the Savile estate denied liability, prompting lawyers to seek disclosure of documents from the police.
Last week Savile's estate, which is reportedly worth £4.3m, was frozen in response to the mounting allegations.
Savile, who died last year at the age of 84, is believed to have been one of the UK's most prolific sex offenders, with about 300 possible victims.
Detectives from Scotland Yard are following 400 lines of inquiry and the BBC has launched an inquiry into the culture and practices at the corporation during the time the abuse allegedly took place.
Savile used his fame to cover up his activities at three hospitals - Leeds General Infirmary, Stoke Mandeville and Broadmoor secure hospital - and was given accommodation at all three
It has emerged that Savile was first invited into the Leeds hospital in 1961 by its chief porter, Charles Hullighan, to help its new hospital radio station, and promptly volunteered as a porter.
At Broadmoor he was appointed as "Honorary Assistant Entertainments Officer", given an office in the grounds of the hospital, a bedroom, which he called his "cell", and his own set of keys to the wards.
The Department of Health is now investigating the background to his appointment in 1988 as head of a task force overseeing the hospital.