Hodgkinson was the son of George Hodgkinson and his wife Julia Beevor, daughter of the Rev. John. Beevor, Rector of Claypole, Lincolnshire. He was educated at the grammar school at Louth, and was admitted an attorney and solicitor in 1839. He was in practice at Newark, in partnership with J. T. B. Pratt, but gave up his legal practice in 1870. He was a director of the Law Life Assurance Co. and the Midland Railway Company and chairman of the London Chatham and Dover Railway. He was also a Justice of the Peace (JP) for Newark and Nootinghamshire.
At the 1859 general election Hodgkinson was elected as a Member of Parliament (MP) for Newark, defeating the sitting Liberal MP the Earl of Lincoln. He was re-elected in 1865 and in 1868, and held the seat until he stood down from Parliament at the 1874 general election.
Hodgkinson died on 15 February 1881, at his home in Newark, aged 62.
Hodgkinson married Alice Harvey, daughter of Robert Harvey of Balderton in 1845.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "N" (part 1)
- Debretts House of Commons and the Judicial Bench 1870
- "Obituaries". The Times. London. 16 February 1881. p. 10.
- "No. 22258". The London Gazette. 3 May 1859. p. 1813.
- Craig, F. W. S. (1989) . British parliamentary election results 1832–1885 (2nd ed.). Chichester: Parliamentary Research Services. pp. 215–6. ISBN 0-900178-26-4.
- "No. 22991". The London Gazette. 14 July 1865. p. 3527.
- "No. 23444". The London Gazette. 24 November 1868. p. 6108.
- Hansard 1803–2005: contributions in Parliament by Grosvenor Hodgkinson
|Parliament of the United Kingdom|
Earl of Lincoln
| Member of Parliament for Newark
1859 – 1874
With: John Handley to 1865
Lord Arthur Pelham-Clinton 1865–1868
Edward Denison 1868–1870
Samuel Bristowe from 1870