Writing in the satirical magazine Punch, the political theorist, commentator and biographer of George Orwell recounts claims from contemporaries of the one-time Methodist preacher, pillar of society and Mayor of Grantham, Lincolnshire, that he "was a notorious toucher-up".
The assaults supposedly took place about 60 years ago, behind the counter of the shop, next to the "splendid mahogany spice drawers with sparkling brass handles (and) large, black, lacquered tea canisters", recalled in her autobiography by Baroness Thatcher, whose decisive endorsement of William Hague as Conservative leader last week has renewed her influence with the Tory right.
"Older teachers," Professor Crick was told by a Grantham friend, "all remembered their difficulty in trying, good women, to steer girls away from taking jobs at his shop.
"They were frightened to hint at the real reason: for he was a figure of real power in the town."
Crick, emeritus professor of the University of London, said that he learnt of the allegations in the mid-1980s, when the then Prime Minister was promoting the Victorian values of thrift and self-reliance that she had admired in her Rotarian father.
Her comments made the left-wing academic realise that he held the seeds of a story that could damage the Conservatives. Before the 1987 general election, he said, he gave the story to a friendly Daily Mirror journalist, who then declined to alert his newsdesk, fearing the wrath of owner Robert Maxwell, should it create too much controversy.
The story remained a secret until it appeared in Punch last week, although he had tried to persuade the magazine to publish it before this year's election.
Lady Thatcher's office said that the former Prime Minister had no comment.
However, although tales of her father's alleged sexual misconduct might not have been known nationally, they have been common currency in Grantham for years, it was clear last week.
Peter Hadlow, 76, lived next-door-but-one to the Robertses, and overheard many conversations about the scandal when working as an apprentice electrician. "Quite a broad spectrum of people said it. It was all over Grantham virtually," he said. "I would hear the boss talking about it. My ears were flapping - that sounds juicy, I thought.
"These stories were bandied about, and eventually you begin to believe there was some truth in them. But he was an Alderman and so that sort of thing got hushed up. It was a question of who do you believe - a teenage girl, or Mr Roberts?"
Mr Hadlow still lives in the same area of the town and added: "Funnily enough, when he gave up running the shop, he changed into a really nice bloke".
More significant still were the comments of a 74-year-old woman from Grantham, who told the Independent on Sunday that she had been molested on frequent occasions by Alderman Roberts, when she worked in his shop, aged just 15.
She said: "He was a bad one. He came round and put his arms around me, feeling my breasts. He used to put his tongue in my mouth.
"I got quite frightened. I didn't like it and I'd push him away. He'd say nothing and go, but then he would come back again. He used to chase other girls round the counter." She worked at the shop for six months until she told her parents what was happening. Her father told her she should not return.
The woman, who does not wish to be named, was then a chorister at the Methodist chapel where Alderman Roberts was a lay preacher. "One Sunday, I got up and walked out. I couldn't stand him standing up there and preaching," she said.
It was only then, when her parents challenged her to explain her behaviour, that she told them about the harassment she had suffered at the hands of the Alderman.
Professor Crick said that his piece was "written in the spirit of good- humoured satiric rage".
He said he had wanted it to be published before the general election. "I was so angry at the Conservative Party using all that family values stuff. To use it for political purposes is really quite off. It debases politics and in the end, you get caught out. It's a great offence to exploit and mythologise the past for political purposes."
Punch also sent a reporter to Grantham, who found pensioners willing to recount lurid tales about the grocer. One elderly resident claimed that she had two cousins working at the shop. "He was forever pinching their bums when they bent over - and looking up their skirts."
Journalist Richard Creasy wrote: "Memories of Alderman Alf raise a smirk amongst the pensioners who remember him far from fondly."
Paul Spike, editor of Punch, said: "People have been talking about this, but no one has been willing to run this until now. Crick has been talking about it for decades - he's a known responsible figure.
"We're not saying this has been established in a court of law. We thought we should check it out further. That's as much as we could get."
The rumours about Alderman Roberts took on fictional form in a novel about Thirties Grantham, Rotten Borough, written by local journalist Oliver Anderson and published in 1937. It featured a councillor who ran a corner grocery shop and was given to frolicking with his female assistants. At one point he is caught in flagrante beside the pork pies and polony sausages when a faulty light is switched on and passers-by see him, trousers down, through the shop window.
Rotten Borough was withdrawn from sale after just three weeks following threats from the Grantham establishment, including an earl and MP, of legal action. In 1989 it was republished by Fourth Estate. Its author died last year.