Bamber, 59, is serving a life sentence for killing his family in the 1985 murders at the White House Farm, the subject of ITV drama this year.
He was convicted of shooting his adoptive parents June and Nevill, both 61, his sister Sheila Caffell, 28, and his six-year-old twins, Daniel and Nicholas.
Bamber is locked up in his cell at Wakefield prison in West Yorkshire. He was not tested positive for the coronavirus and showed no symptoms.
He wrote in a blog post: “We, like all of you, follow strict social distancing measures in the prison.
“So, with the extra time to work in my cell, I’m preparing an additional project with campaign administrator Yvonne Hartley.
“We work very well together on the material of the case and there is much more to discover. “
Yvonne, 53, said she last spoke to Bamber on Thursday on a phone call. She said, “We discovered new things while studying the material.
“The case is constantly evolving and we are still working on the appeal of the Criminal Matters Review Board.”
Bamber’s legal team is preparing a submission to the CCRC with the desperate aim of referring his case to the Court of Appeal.
They are first waiting to hear an application for judicial review against the Crown, following allegations that prosecutors refused to release key documents to the defense during the 1986 trial.
The six-part series White House Farm, with Freddie Fox, 31, like Bamber, started in January and told the story behind the killings and the botched police investigation.
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In January, we told how Bamber claimed that he had discovered new evidence showing his innocence, including recordings of telephone calls, and evidence that there was someone alive at White House Farm long after that the whole family would be dead.
Bamber still maintains that 26-year-old Sheila, schizophrenic, killed his family before turning the gun on himself.