Sir Basil Rawdon Jackson (died March 1957), was a British businessman, chairman of BP from February 1956 to June 1957. Jackson was deputy chairman of BP, and in 1956 succeeded William Fraser, 1st Baron Strathalmond as chairman. He stepped down due to poor health in January 1957 and died in March the same year. In 1957, he was succeeded by Neville Gass as chairman of BP.