Born as Brenda Mary Hugh-Jones, daughter of Llewellyn Arthur Hugh-Jones, Governor of Faiyum in Egypt, and Dulcibella Eden, a cousin of Anthony Eden, she was educated at Queen Anne's School, Caversham. She earned a scholarship to attend Oxford University, but left without graduating, in order to join her father in Cairo.
In 1939, she enlisted in the ATS Officer Cadet training unit, but soon left to work for the Ministry of Economic Warfare in London. Through mutual friends she met Flt Lt Derek Rawnsley, who had made history by flying solo in a Tiger Moth from Australia to Oxford. In 1937 Lt Rawnsley had founded the Federal Union Movement with Charles Kimber and Patrick Ransome, seeking the unification of Europe to avoid war. Hugh-Jones and Rawnsley were married in February 1941, but he was immediately posted overseas in the RAF. By the end of 1941, Mrs Rawnsley was a Women's Auxiliary Air Force officer. Fluent in French, Arabic and Greek, she was of great importance and sent in 1942 to Heliopolis, and later, to RAF Ramleh in the then-British Mandate in Palestine.
Lt Rawnsley was killed in a February 1943 accident, after which Mrs Rawnsley worked with 201 Squadron, Alexandria and was subsequently posted to Algiers in February 1944 to work with Gen. Wilson, the Commander-in-Chief of the Allied Forces in the Middle East. Later she returned to England to work with Duncan Sandys, trying to forecast the course of flying bombs (V1s) and rockets (V2s). In June 1945 she was dispatched on an intelligence mission to the German flying bomb factory in the Harz Mountains, and subsequently wrote a history of the flying bomb for the Air Ministry, leaving the service with the rank of squadron leader and a variety of medals in 1945.
In 1935, with the backing of Sir Philip Sassoon, Derek Rawnsley had set up Picture Hire Ltd., which made available for rent original pictures by contemporary artists, and School Prints Ltd., which aimed to loan sets of reproductions to schools so that children could learn about the world's great works of art. With the support of Victor Bonham Carter and architect Raglan Squire she followed her late husband's goals of bringing "good" art to schoolchildren who otherwise would not have had the opportunity to enjoy it.
In her introductory letter to artists she wrote: "We are producing a series of auto-lithographs, four for each term, for use in schools, as a means of giving school children an understanding of contemporary art." The majority of the prints were lithographed directly by almost two dozen artists and printed by the Baynard Press. To minimise framing costs, each picture included a decorative border, and they were distributed to schools in redundant cartridge cases bought from the Ministry of Supply.
In 1949 she married Geoffrey Keighley, and they had one son. The couple divorced in 1952. Brenda Keighley also continued the original idea of lending out works, expanding it in the 1950s to "Pictures for Industry", which offered 700 prints for display in factories and workplaces, and "Pictures in Hospitals". In 1971 The Observer agreed to sell the remaining stocks of the European series and the rest of the business was sold to Patrick Seale, the paper's Middle East correspondent. Rawnsley was elected to the position of Master of the Fine Art Trade Guild (1961–62). She subsequently worked as a librarian before retiring to Hampshire, where she died, aged 90.