Smith, who died in 2010 aged 82, reportedly bonded with Savile after meeting him at a medieval banquet forty years ago.
In his autobiography Big Cyril, the MP whom police have now acknowledged abused young boys, recounts meeting the DJ.
He said: "I once attended a medieval banquet at Worsley, Lancashire, along with Jimmy Savile. When I joined in the community singing, Jimmy blurted out: 'You've got a nice voice there, Cyril, you must come on my programme!' That's how I ended up singing 'She's a Lassie from Lancashire' on Clunk Click."
This week Greater Manchester Police (GMP) admitted there was "overwhelming" evidence the 28-stone MP sexually and physically abused young boys in the 1960s.
The former MP for Rochdale was elected to parliament in 1972 and was dogged by rumours of abuse throughout his career, although charges were never brought.
According to GMP, which has now assumed full responsibility for the case, prosecutors were given evidence about Smith three times - in 1970, February 1998 and March 1999 - and each time missed their chance.
Police are investigation allegations Savile abused children throughout his career as a DJ and TV personality.
Police are following 400 lines of inquiry as part of the investigation into Savile's activities, and the BBC has launched an inquiry into the culture and practices at the broadcaster during the era of the alleged abuse.
Jimmy Savile in 1961 around the time he was working for Radio Luxembourg. He is at London Airport with Pan American stewardess Birgit Johansson with two gold discs; one is for American singer Elvis Presley for having sold one million copies of "It's Now or Never" in the UK, and the other is for Presley's manager, Colonel Tom Parker
Cilla Black and Jimmy Savile before a Variety Club Luncheon at the Savoy Hotel. Taken in 1964, the year Savile became the first presenter of Top of the Pops
Two women have come forward with allegations from the 1960s, one who was 14 and another who was a teenager when she claims Savile sexually abused her in Scarborough
Savile in 1969 with Physically Handicapped and Able-Bodied (PHAB) member Erika Mentz from Germany and other PHAB members at a dance at Devonshire House
1969 also saw Savile begin volunteering at the Stoke Mandeville Hospital for specialist spinal injuries. He would later be given a room there
Jimmy Savile presenting a cheque to children on behalf of the NSPCC in 1969
The 1970s saw Savile start volunteering at Leeds General Infirmary and...
... Broadmoor secure high-security psychiatric hospital. Allegations by former patients have been made against Savile although ex-workers have disputed the idea that he could have been left alone with anyone whilst working there
The 70s also saw the start of Jim'll Fix It. Allegations from this period include Caroline Moore, a 13-year-old patient at Stoke Mandeville hospital in 1971, who says Savile "rammed his tongue" down her throat and another allegation accuses Savile of molesting a brain-damaged teenage patient at Leeds General Infirmary in 1972
The 1980s saw the continuation of Top of the Pops and Jim'll Fix It as Savile became a much loved household name. Two allegations relating to this time include one from a then-15-year-old girl (not pictured) who made a complaint of abuse by Savile in Lancashire. Pictured is 12-year-old Rebecca Heap
Savile at the Stoke Mandeville hospital with injured children from Beirut in 1987
Savile was knighted in 1990 and continued his charity work throughout the decade
Savile was questioned in 2007 by police about allegations of sexual abuse but the Crown Prosecution service says there is not enough evidence to warrant a prosecution
A 2008 police report into abuse at the Haut de Garenne children's home in Jersey names Savile, although this is never made public
Savile re-united with his Jim'll Fix It chair in 2009. The previous year Sussex police received a complaint of sexual assault but went on to say the victim was "unwilling to co-operate in any investigation"
Jimmy Savile is found dead at the age of 84 in October 2011. He is buried in Scarborough
In December 2011 the BBC drop an investigation by Newsnight into the allegations of sexual abuse by Jimmy Savile. Three tribute programmes are aired instead
ITV airs a documentary, 'Exposure, the Other Side of Jimmy Savile', in which a number of women claim they were abused by Savile as youngsters, including Karin Ward (pictured)
Within days of the documentary, many more allegations surface. By the 9 October Peter Spindler of the Metropolitan Police tells the BBC: "It is quite clear from what women are telling us that Savile was a predatory sex offender"
11 October 2012 and George Entwistle, Director General of the BBC, asks journalists why the Newsnight programme was dropped as police from Tayside, Greater Manchester, Lancashire and North Yorkshire police say they are investigating allegations going back to 1959
12 October and police reveal they have 340 potential lines of inquiry
15 October sees a man come forward alleging that Savile abused him when he was a nine-year-old boyscout
Savile's family removed his headstone from his grave and broke it up in the wake of the furore
Jimmy Savile sexually abuses transgender man
A transgender man comes forward alleging that Jimmy Savile 'stuck his hand up his nightdress' while he was a 17-year-old teenage girl at Broadmoor in the 1970's. More here http://www.huffingtonpost.co.uk/2012/10/15/jimmy-savile-timeline-abuse-allegations_n_1966426.html?1350304573#slide=1641388