Died 1777. He was the father of Admiral Philip Wilkinson-Stephens.
Wilkinson was commissioned lieutenant on 22 August 1759.
He was promoted commander on 4 September 1766 of the Hound 10, although she was paid off that month, and in early 1768 commissioned the new Swan 14, going out to Newfoundland in April, serving in the Mediterranean and home waters during 1769, and being employed off Scotland in the following year.
He was posted captain on 10 January 1771, and after brief spells aboard the Monarch 74 at Chatham and Fowey 24 at Sheerness he commanded the Winchelsea 32 in the Mediterranean from the summer of 1772 until she was paid off at Sheerness in June 1775.
In the spring of 1776 Wilkinson joined the Pearl 32, and taking her out to North America he participated in the campaign to capture New York from July to October. He managed to capture a number of rebel vessels, including the brig Lexington 16 on 19 December, although she was later re-taken from the prize crew he had put aboard.
The Pearl having sailed for the Leeward Islands, Captain Wilkinson died there in early 1777.
He married Millicent Howe of Mistley Thorne, Essex, who following his death married a Gabriel Matthias of Scotland Yard, London. She was the sister of Captain William Howe who died in 1765, and of Captain Tyringham Howe who died in 1783, and was also the niece of Sir Philip Stephens, the influential first secretary to the Admiralty from 1763-95. Their only son was Admiral Philip Wilkinson-Stephens.