Smiths death was confirmed by her sons Toby Stephens and Chris Larkin.
An intensely private person, she was with friends and family at the end.
Hugh Bonneville, SmithsDowntonco-star, told the BBC that she was a true legend of the acting community.
PBS
In all, she won a record six Evening Standard awards for her stage performances.
Smith was married to Robert Stephens between 1967 and 1974.
She later wed Beverley Cross in 1975 and remained his wife until his death in 1998.
Her sons Stephens and Larkin both followed her into the acting profession.
Greg Evans contributed to this report.
