Plater's agent tells the BBC he had been "very robust" until he was checked into a London hospice for his last week of life.
His career spanned six decades, during which time he wrote numerous works for the stage and screen as well as six novels.
Plater received a BAFTA award for writing in 2005 and he accepted a lifetime achievement honour from the Writers' Guild of Great Britain in 2007.
Among the full-length dramas he wrote was 2000 movie The Last of the Blonde Bombshells, which starred Dame Judi Dench in the lead role.
His final screenplay was World War II drama Joe Maddison's War, which will air on U.K. TV later this year (10).