Hammond was born Mavis Chin to a Chinese father from Guangdong, and a Jamaican mother in Tweeside, Clarendon Parish. She moved to the United Kingdom in 1959 on a Jamaican Scholarship and worked for Norman and Dawbarn Architects. She attended evening classes at the City Literary Institute in London for two years and was awarded a scholarship to the Royal Academy of Dramatic Art.

Hammond began her career on stage and made early appearances on television shows such as Softly, Softly (1968) and The Trouble Shooters (1969). Her first leading role was as Lady Macbeth at the Roundhouse in 1970 in Peter Coe's African version of the play. She went on to star in many plays by an array of up-and-coming black writers: Sweet Talk by Michael Abbensetts, 11 Josephine House by Alfred Fagon and several plays written by Mustapha Matura including As Time Goes By, Play Mas and Playboy of the West Indies. She also spent two years at the Royal National Theatre in productions including Fuente Ovejuna and Peer Gynt directed by Declan Donnellan, and The Crucible.

Television work followed, which included roles in The Sweeney (1976); Wolcott (1980–81), a three-part ATV mini-series about a black detective based in East London; Black Silk (1985); Juliet Bravo (1985); Playboy of the West Indies (1985), Casualty (1986) and When Love Dies (1990).

In 1985 Hammond along with Yvonne Brewster, Inigo Espejel and Carmen Munroe founded Talawa Theatre Company, which became one of the UK's most prominent black theatre companies. It has produced award-winning plays from and about the African diaspora and has championed reinterpretations of classical British pieces. Hammond performed in several of its productions including The Black Jacobins, The Importance of Being Earnest and King Lear.

Hammond appeared as Shirley Armitage's mother, Velma, in the ITV soap opera Coronation Street in 1988.

Hammond has played many roles in television sitcoms, including: Susu in Desmond's (1990–94) and its spin-off Porkpie (1995–96); Us Girls (1992–93), in which she played Grandma Pinnock; Chef! (1996), and Grandma Sylvie Headly in The Crouches (2003–05).

Hammond has appeared in ITV's Coronation Street, twice, first playing the role of Jan Sargent and the second time playing Mrs Armitage, mother of Shirley Armitage. In 1994 she was cast as Blossom Jackson in BBC's EastEnders. She remained in the role until 1997. This was Hammond's second role in the soap, having previously played the minor part of Michelle Fowler's midwife in 1986.

In 1999 she played the role of Nan in the children's TV series Pig-Heart Boy, based on a novel by Malorie Blackman. Hammond's other television credits include Making Out (1989); Trial & Retribution (1998) as Bibi Harrow: Sunburn (1999); Storm Damage (2000); The Bill (2001); Babyfather (2001); White Teeth (2002); A Touch of Frost (2003); Holby City (2001; 2005; 2011); Doctors (2006) and Death in Paradise (2011). She also appeared in the Doctor Who episode "Rise of the Cybermen" in 2006. Her film credits include Fords on Water (1983), Manderlay (2005) and Kinky Boots (2006). Hammond appeared in the 2008 movie 10,000 BC, directed by Roland Emmerich.

Hammond was appointed an Officer of the Order of the British Empire (OBE) in the 2005 Queen's Birthday Honours List, for her services to drama in the UK. In 2006 Hammond was presented with the Edric Connor Inspiration Award - the Screen Nation Film and Television Awards' highest UK honour.

For a brief stint in October 2010, she reprised her role as Blossom Jackson in EastEnders: appearing in connection with screen great-grandson Billie Jackson's funeral, she returned with her on-screen grandson Alan Jackson.