Born in Bethnal Green, London, he was the son of Eugene Bernard Bellenger, a dairyman, and his wife Isabella Annette née Henner. He received only an elementary education before starting work aged 14. He worked in various jobs: in a tea warehouse in Houndsditch, as a messenger boy for the Post Office and as a clerk to an export company in the City of London.
With the outbreak of the First World War in August 1914, Bellenger volunteered to join the British Army. He became a gunner in the Royal Field Artillery, arriving at the Western Front in the following year. He was twice wounded, and rose through the ranks, being commissioned as a second lieutenant in 1917. Following the armistice in November 1918, he served in the forces occupying the Rhineland. He was demobilised in 1919.
In Cologne he had met Marion Theresa Stollwerck, daughter of Generalkonsul Karl Stollwerck, a wealthy German chocolate manufacturer, and they married in 1922. They had five sons and one daughter.
Following the war he worked as a surveyor and estate agent in west London. He became active in the local Conservative Association, and was elected to Fulham Borough Council as a Municipal Reform Party councillor representing Baron's Court ward in 1922 and 1925. He did not stand for election in 1928, and shortly afterwards joined the Labour Party.
In June 1930 he was selected by the Labour Party as their prospective parliamentary candidate at Bethnal Green South West, but withdrew his candidature a year later on health grounds. When the Labour Party split over the formation of a National Government in August 1931, he remained with the majority faction opposing the move.
In November 1933 he was chosen to contest Bassetlaw in Nottinghamshire, a seat held by Malcolm MacDonald, son of National Labour Organisation leader Ramsay MacDonald. At the 1935 general election he won the seat, and held it comfortably at each election until his death.
Bellenger remained in the army's emergency reserve, and when the Second World War broke out in 1939 he was automatically recalled to service. He was commissioned as a captain in the Royal Artillery in February 1940. He went to France as a staff officer in April of that year as part of the British Expeditionary Force. He returned to the United Kingdom briefly in May to take part in the Norway Debate in the Commons that led to the fall of Neville Chamberlain's government. Evacuated from France in June 1940, two months later he resigned his commission. Apart from his parliamentary activities, Bellenger wrote a column for the Sunday Pictorial under the byline "Voice of the Services".
When the Labour Party won a landslide victory at the 1945 general election, he was appointed Financial Secretary to the War Office. In October 1946 he became Secretary of State for War. Although not a cabinet position he was appointed a Privy Counsellor at the same time. He proved an unpopular minister with Labour backbenchers, and was attacked by those on the left of the party. It came as no surprise when he lost office at a ministerial reshuffle in October 1947.
Bellenger remained on the Labour backbenches for the rest of his life. He became increasingly disconnected from the mainstream of the party, being unsympathetic to trade unions, opposing the decriminalisation of homosexuality and supporting the Unilateral Declaration of Independence by white Rhodesians. Following the 1966 general election the Bassetlaw Parliamentary Labour Party deselected him over his opposition to steel nationalisation and position on Rhodesia.
However, Bellenger was still Bassetlaw's MP when he died at his Kensington, London, home in May 1968, aged 73. He had received the honorary freedom of the Borough of Worksop two days earlier.