Her father was Captain (brevet Major) William Degacher (1841–1879) of the 1st Battalion, 24th Regiment of Foot, who was killed at the Battle of Isandlwana during the Anglo-Zulu War in 1879.

Niven's father, a lieutenant in the Berkshire Yeomanry of Scottish descent, was killed in action in Turkey during the Gallipoli Campaign of the First World War on 21 August 1915.

[11] The family moved to Rose Cottage in Bembridge on the Isle of Wight after selling their London home, where Grizel and David played cricket and sailed in a dinghy during school holidays.

[15] After completing her studies at RADA, Niven joined a touring theatre group, acting alongside Jean Anderson, Robert Morley, and Sir John Clements.

[4][15] As a sculptor, Niven was influenced by the abstract figures of Henry Moore, although she also created portrait sculptures including a "naturalistic" bust of her brother David.

[15] Her interest in architecture and the way that light is reflected off buildings led her to experiment with metal strips on Perspex or card; she also created black-and-white paintings and drawings which she called Catoptrics.

[1] In 1959, Niven, in collaboration with architect Paul Clinton, was awarded a £100 prize for one the six best designs in an international competition for the memorial sculpture at the Dachau Concentration Camp.

[17][18][19] Their entry, the only one from England, was described as "an open square surrounded by a double wall of dark grey stone with the sculpture of two hands reaching for the sky in the centre".

[18][19] In 1980, Niven's studio in Fulham was broken into by a burglar who stole valuables, including her carving tools for wood and stone, and smashed everything in sight.

[26][25] When Bessie debuted as the Orange Women's Prize for Fiction trophy in 1996, The Daily Telegraph described it as "what sounds like a frightfully politically incorrect bauble – a bronze statuette of a nude woman, boasting prominent breasts".

[26] In 2001, critic Helen Brown described the statuette in the same paper as "a small, female figure with a surface texture resembling the inside of a golf ball and peculiarly high-sitting breasts".

[25] Niven remained close to her brother David throughout his life, accompanying him to dinner with Elizabeth Taylor and producer Mike Todd, and to drinks with Jackie and John F. Kennedy before he became president.