Web sites hosting violent sexual content, partially blamed for setting Graham Coutts on the road to murder, may be outlawed.
Brighton MP David Lepper is to lobby Government ministers, demanding they make using the web pages illegal in the same way as downloading child porn.
Coutts spent years viewing pictures and films of strangulation, rape, murder and necrophilia on the net.
They fuelled his sick fantasies and, he admitted, made him feel more normal.
Sussex Police and Jane's family have joined the call for action.
Jane's partner, Malcolm Sentance, 35, said controls would be difficult but added: "I think Jane would have been here if not for the internet."
Her mother, Liz Longhurst, 72, said: "Pressure should be put on internet service providers to close down or filter out these pornographic sites which have played such a prominent part in this trial, so people like Jane's killer may no longer feed their sick imaginations and do harm to others."
Jane's sister, Sue Barnett, 40, said: "The last ten years has seen an explosion of pornography on the internet. The next ten years must see some regulation."
Grace Blaker, a Lewes resident and friend of the Longhurst family, is asking local MP Norman Baker to support the campaign.
Detective Inspector Chris Standard, second-in-command of the murder hunt, said: "I would like to see a crusade to clean up the internet. I am sure such material contributed to Jane's murder."
Mr Standard said governments around the world had to take joint action.
He wants a ban on web providers handling such material and on search engines allowing the sites to reach the internet.
The Argus took less than two minutes and just a few mouse-clicks to find the sick sites Coutts was looking at.
Mr Lepper, MP for Brighton Pavilion and a former teacher at Uplands School where Jane worked, said: "There is real concern. We need much tighter regulation, self-regulation preferably.
"I know libertarians would say this should be left to viewers and I realise the internet is tremendous for obtaining information but there is a good case for regulating this particular material."
Mr Sentance said he owed it to Jane to fight for a ban.
Her family said it was the only good thing that could ever come from her death.
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