Greville was the second son of Francis Greville, 1st Earl of Warwick, by Elizabeth Hamilton, daughter of Lord Archibald Hamilton. George Greville, 2nd Earl of Warwick, and Robert Fulke Greville, were his brothers.
Greville lived on a stringent income of ₤500 a year, but managed to acquire antiquities from Gavin Hamilton in Rome. He also purchased through his uncle a genre piece by Annibale Carracci. As a Fellow of the Royal Society, his special interest was in minerals and precious stones, which were catalogued by the émigré Jacques Louis, Comte de Bournon, and were later purchased via Act of Parliament for the British Museum. He was good friends with James Smithson, whom he sponsored for membership in the Royal Society and with whom he exchanged minerals.
Greville remained for years a very close friend of Sir Joseph Banks and, like him, a member of the Society of Dilettanti. He accompanied Banks at the organizing meeting in March 1804 of the precursor to the Royal Horticultural Society, the Society for the Improvement of Horticulture.
The nephew of Sir William Hamilton, the British envoy at Naples who formed two collections of Greek vases, one of which is at the British Museum, Greville briefly (1782–86) had for a mistress Emma Hart, whom he educated and took to George Romney’s studio where he was sitting for his own portrait; Romney became fascinated with the beautiful Emma, who later became Sir William’s Lady Hamilton and eventually Lord Nelson’s lover.
When his father died in 1773 and his brother became Earl of Warwick, Greville inherited his seat of Warwick in the House of Commons. He held the seat until 1790. He served as a Lord of the Treasury from 1780 to 1782, as Treasurer of the Household from 1783 to 1784 and as Vice-Chamberlain of the Household from 1794 to 1804 and was sworn of the Privy Council in 1783.
The construction of the seaport of Milford Haven, Pembrokeshire, South Wales, is due to Greville’s entrepreneurial spirit. When it was the property of Sir William Hamilton, Greville applied for an Act of Parliament to enable Hamilton and his heirs to make docks, construct quays, establish markets, with roads and avenues to the port, to regulate the police, and make the place a station for conveying the mails. The first structure was a coaching inn. Natives of Nantucket were induced to settle, and for some decades Milford was a whaling port. A royal dockyard was established during the Napoleonic Wars. At his death in 1803, Hamilton bequeathed it to his nephew.
Greville never married. He lived for years in a house facing Paddington Green, then a suburban district of London, where he indulged his passion for gardening in a large garden provided with glasshouses in which he grew many rare tropical plants, aided by his connection with Banks, and where he managed to coax Vanilla planifolia to flower for the first time under glass, in the winter of 1806-07. His contributions to the herbarium assembled by Sir James Edward Smith are preserved by the Linnaean Society of London. The Australasian genus Grevillea is named in his honour. In the latter part of his life he lived at Warwick Castle.
Greville died in April 1809, aged 60. Greville Island, in the South Island of New Zealand, was named to honour his memory by Ensign Barallier, in 1820. Greville plays a role in Susan Sontag’s 1992 novel The Volcano Lover, about Sir William Hamilton.