He was the eldest surviving son of Henry Godolphin, provost of Eton and Dean of St Paul’s, and was educated at Eton College (1718–1721) and Queen’s College, Oxford (1723). In 1733 he succeeded to his father's estates in Buckinghamshire.
He was appointed Lieutenant-governor of the Scilly Isles from 1739 to 1766 and full Governor from 1766 to his death. He was also recorder for Helston from 1766 to his death.
He was elected a Member of Parliament (MP) for the borough of Helston in Cornwall from 1741 to 1766, when he succeeded to the Barony of Helston on the death of his cousin Francis Godolphin, 2nd Earl of Godolphin.
He married twice: firstly to Lady Barbara Bentinck, the daughter of William Bentinck, 1st Earl of Portland, and secondly to Lady Anne Fitzwilliam, the daughter of John Fitzwilliam, 2nd Earl Fitzwilliam. He had no children.
- "GODOLPHIN, Francis (1706-85), of Baylis, Bucks". History of Parliament Online. Retrieved 14 June 2016.
- Stooks Smith, Henry. (1973) [1844-1850]. Craig, F. W. S. (ed.). The Parliaments of England (2nd ed.). Chichester: Parliamentary Research Services. p. 39. ISBN 0-900178-13-2.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "H" (part 2)
|Parliament of Great Britain|
| Member of Parliament for Helston
With: Thomas Walker
Sir John Evelyn
Sir John Evelyn
The Earl of Godolphin
| Governor of the Isles of Scilly
Marquess of Carmarthen
|Peerage of Great Britain|
| Baron Godolphin
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