Local businessman and Savile’s lifelong friend, James Corrigan, said it would be a “fitting” memorial for the broadcaster who loved the Yorkshire resort ever since he went there for childhood holidays.

Corrigan said: “”The most fitting tribute would be a statue paying tribute to him and what he’s done for this area.”

Leeds-born Savile, who was known for presenting Jim’ll Fix It and Top of the Pops, had a home on the resort.

Conservative leader of Scarborough Borough Council, Tom Fox said the council would consider the proposal.

He added: “You couldn’t buy the publicity he brought to the town. It was his adopted home and he became one of the town’s adopted sons.”

Savile, who was found dead at his home in Leeds on Saturday, aged 84, lived by his mantra: “If it ain’t a game it’s a shame”.

Louis Theroux said of the star: “Jimmy loved to entertain, to dazzle, and to joke. And in an age of agents, PRs, and media handlers, he was completely the opposite – utterly free of showbiz airs and as far from being a diva as one could imagine.”

A book of condolences was set up in Savile’s Hall opposite Leeds Royal Armouries Museum.

Friends insisted he did not die a loner, but that he had plenty of friends.

Savile was best man for Howard Silverman, 59, who said Jimmy used to hold a Friday Morning Club at his flat, where friends would be invited to enjoy tea, cakes and whisky.

Savile also worked relentlessly to raise money for charity, making a total of £40 million for various causes.