News of Fiennes's affair appears to explode the couple's reputation for having a strong relationship - a reputation of which they have been fiercely protective in the face of rumours to the contrary.
Fiennes recently threatened legal action after gossip columnists in New York linked him to the actress Gina Gershon, star of the film Showgirls.
And four years ago, the actor was caught canoodling with Jennifer Lopez, his co-star in Maid In Manhattan.
Fiennes and Miss Annis met when they starred together in Hamlet at the Hackney Empire in 1995. Fiennes was in the title role while Miss Annis was playing his mother Gertrude.
Both were involved in long-term relationships at the time - she with the photographer Patrick Wiseman, father of her three children, while Fiennes was married to Miss Kingston.