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In the year 1747, Lord Viscount Dunkerron became possessed of a capital messuage at Turnham Green, which having passed through various hands, viz., the Earl of Kerry (1752), Matthew Hutton, Esq (1762), the Earl of Egmont (1765), Sir Brownlow Cust (1771), the Duchess of Devonshire (1772), Lord John Cavendish (1777), was purchased in 1789 by Lord Heathfield, the celebrated defender of Gibraltar, who made it his principal residence till his death, which happened not long afterwards: it belonged lately to Dr. Alexander Meyersbach, and is now the property and residence of Mrs. Wildman. The gardens were laid out with much taste for Lord Heathfield, by Mr. Aiton, now His Majesty's gardener at Kew.
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It is stated that Simon Fraser, Lord Lovat, the Scottish rebel, who was executed for his share in the troubles of 1745, lived in a house on this spot, and the Rev. S. Arnott, in a contribution to "Notes and Queries," June, 1880, remarks this, and calls attention to the fact of 1747 being the date of his execution, which would appear to confirm the statement. The house stood at the south-west corner of Turnham Green, near the site of the present vicarage, and Heathfield gardens occupies the site of the grounds; a portion of the old wall which surrounded it still stands at the northern end of Sutton-lane, as do the brick piers surmounted by stone balls of the old gateway, the space after the removal of the gate to the Duke of Devonshire's being walled up. The house is chiefly remarkable as being the residence, till his death, of General Elliott, Lord Heathfield, the celebrated defender of Gibraltar. It was pulled down in 1837, and the site for many years laid waste. A view of the house is to be found in Faulkner.
The handsome iron gates which stand at the end of the Duke's-avenue and form one of the entrances to the grounds of Chiswick House were formerly the property of Lord Heathfield, and stood at the entrance of his grounds, at the south-west corner of Turnham Green. Upon the demolition of Heathfield House in 1837, they were bought by the Duke of Devonshire, and removed to their present position. Two brick piers, which still remain as part of the garden wall of Turnham Green Vicarage, mark their original site.
[In 1897 the gates were removed to Devonshire House, Piccadilly. They were erected in Green Park in 1921 after Devonshire House was demolished.]
You can see the gates as they appear today here.
Source: Historical Collections Relating to Chiswick Edited by W.P.W. Phillimore and W.H. Whitear, London, 1897
Source: English Heritage