Graham, who is the older brother of actor and director Dexter Fletcher, was diagnosed with mesothelioma in February 2018 and died 15 months later.
In court papers, Jeanette’s QC Michael Rawlinson claims Graham “was regularly brought into contact with substantial quantities of asbestos dust”, during his time working at the BBC.
He continued: “The sets were often constructed from fireproof insulation board containing asbestos dust.”
The barrister representing Jeanette went on to say the sets were “modified” or moved by technicians while Graham was on set.
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“In general, if there was any extended break for scenery to be fabricated Mr Fletcher would have been stood down to the Green Room,” defence QC David Platt stated.
A spokesperson for the BBC declined to comment when approached by Express.co.uk.
Graham acted in a variety of productions such as Casualty, Survivors, Nicholas Nickleby and Play for Today.
As well as this, he appeared in Bugsy Malone, Sid and Nancy, Cry Freedom and The French Lieutenant’s Woman.