When one art society once referred to her as Miss Gluck, she was furious and threatened to resign as a member.
Gluck’s self-portrait was recently used as the poster image for an exhibition at Tate Britain which marked the 50th anniversary of the 1967 Sexual Offences Act which partially decriminalised male homosexuality in England and Wales.
Throughout her life the artist had several relationships with high-profile women of her time.
Historic England welcomed the initiative, which will re-ilst Gluck's Sussex home.
Heritage Minister John Glen said: “It is vital that we remember all the communities that have shaped our past.
“I am delighted that we are recognising the significant contribution made by these outstanding people and protecting the places where they lived and worked for future generations.”