Beckett was the son of William Beckett-Denison MP. He was educated at Eton College and joined the family banking business, Beckett & Co, in Leeds. After the firm was taken over by the Westminster Bank he joined the bank's board. He was also chairman of the Yorkshire Post and proprietor and editor of the Saturday Review. His elder brother, Ernest, succeeded his uncle as 2nd Baron Grimthorpe in 1905 and Beckett was granted the precedence of a baron's son and the right to use the style "The Honourable".
He was elected at the 1906 general election as Member of Parliament for Whitby. When that constituency was abolished for the 1918 general election, he was returned for the new Scarborough and Whitby constituency. He did not contest the 1922 general election, but returned to the House of Commons at the 1923 general election as Member of Parliament for Leeds North, and held that seat until he retired from Parliament at the 1929 election.
Beckett was commissioned a Lieutenant in the 3rd (Militia) Battalion, Green Howards in 1884, but resigned his commission in 1886. He was commissioned a Second Lieutenant in the Yorkshire Hussars in 1888. He was promoted Lieutenant in 1895 and Captain in 1898, and resigned his commission in 1901 During the First World War he returned to service as Assistant Military Secretary of Northern Command from 1914 to 1916. He was Assistant Director of the Department of War Trade from 1918 to 1919.
He married the Honourable Mabel Theresa Duncombe (1877–1913) the daughter of William Duncombe, Viscount Helmsley. They had four daughters:
- Marion Frances Theresa Beckett (8 Nov 1896 – 2 Feb 1972) married Vice-Admiral Henry Jack Egerton, son of Charles Augustus Egerton and Lady Mabel Annie Brassey, on 16 October 1919
- Cynthia Maud Beckett (15 Dec 1900 – 25 Dec 1969) married Captain John Arthur Davison, son of Major Arthur Pearson Davison, on 10 November 1919. Divorced 1928. She married German author and BT-correspondent Kurt Hermann Paul Otto Valerio Baron von Stutterheim (1888-1978), son of Richard Karl Ludwig Baron von Stutterheim, on 10 July 1929. Divorced in 1952.
- Beatrice Helen Beckett (26 Jul 1905 – 29 Jun 1957) – married Anthony Eden.
- Ann Prunella Beckett (16 Sep 1907 – 17 Mar 2001) married Lt.-Col. Harry Rumbold Bathurst Norman, son of Reverend Harry Bathurst Norman, on 15 April 1936.
Secondly he married Lady Marjorie Blanche Eva Greville, daughter of Francis Richard Charles Guy Greville, 5th Earl of Warwick and Frances Evelyn Maynard, on 1 November 1917. Lady Greville was the widow of Charles Duncombe, 2nd Earl of Feversham, his first wife's brother. This marriage produced one son:
- Sir Martyn Gervase Beckett, 2nd Bt (6 Nov 1918 – 5 Aug 2001)
- "No. 25349". The London Gazette. 2 May 1884. p. 1983.
- "No. 25646". The London Gazette. 19 November 1886. p. 5599.
- "No. 25776". The London Gazette. 13 January 1888. p. 361.
- "No. 26621". The London Gazette. 3 May 1895. p. 2555.
- "No. 26996". The London Gazette. 16 August 1898. p. 4939.
- "No. 27311". The London Gazette. 7 May 1901. p. 3132.
- "No. 29082". The London Gazette (Supplement). 23 February 1915. p. 1952.
- "No. 29621". The London Gazette. 13 June 1916. p. 5829.
- "No. 32346". The London Gazette (Supplement). 4 June 1921. p. 4530.
- Leigh Rayment's list of baronets
- Leigh Rayment's Historical List of MPs
- Obituary, The Times, 25 August 1937
- Craig, F. W. S. (1983) . British parliamentary election results 1918-1949 (3rd ed.). Chichester: Parliamentary Research Services. ISBN 0-900178-06-X.
- Hansard 1803–2005: contributions in Parliament by Gervase Beckett
|Parliament of the United Kingdom|
| Member of Parliament for Whitby
|New constituency|| Member of Parliament for Scarborough and Whitby
Hugh Myddleton Butler
| Member of Parliament for Leeds North
|Baronetage of the United Kingdom|
|New creation|| Baronet
of Kirkdale Manor, Yorkshire
Martyn Gervase Beckett