He was educated at Hartley College, Church Missionary Society Ladies" College, Colombo and Trinity College, Kandy. After school he joined the University of Ceylon, Colombo from where he graduated with a degree in English, History and Economics.
He was the Inspector General of Police and Sri Lankan Ambassador to Indonesia. He played cricket and rugby for the university too. Rajasingham married Sita.
They had a daughter (Sharminie).
Rajasingham joined the Ceylon Police Force in 1949 as a probationary Assistant Superintendent of Police. He worked at several police stations including Tangalle, Mannar and Colombo.
He rose up the ranks and in 1982 he was appointed Inspector General of Police, the most senior police officer post in the country. He was a Sri Lankan representative at the Thimpu peace talks with Sri Lankan Tamil militant groups in 1985.
Rajasingham was head of the Police Sports Club and its rugby section.
He also played for Ceylonese Rugby & Football Club, served as its president in 1971 and made life member in 1974. After retirement Rajasingham was appointed Sri Lankan Ambassador to Indonesia in 1985. Rajasingham was president of Sri Lanka Rugby Football Union between 1993 and 1994.
Rajasingham died on 24 March 2006 at the Police Hospital in Colombo.
He was a school prefect and member of the cricket and rugby teams at Trinity College. He was later chairman of the State Mortgage Bank and a member of the first Commission to Investigate Allegations Bribery and Corruption.