Sir Antony joined the RSC in 1982 and remains an honorary associate artist with the theatre company.
He has held many leading Shakespearean roles over the years, most recently taking on King Lear at the Barbican in 2016.
He has also portrayed some Jewish characters, taking the lead role in a stage adaptation of Primo Levi’s Shoah memoir If This Is a Man at the National Theatre in 2004 and playing Phillip Gellburg in a production of Broken Glass in 2011.
The two-time Laurence Olivier award winner was knighted in 2000 for services to acting and writing.
The RSC said it would be making “no further comment regarding this personal matter, and we ask that Gregory and Antony’s privacy is respected at this difficult time.”
