The identification of the pamphlet's "Mr. Percival" with Spencer Perceval is not certain; but since no other candidate has presented himself, "Mr. Percival" will be tentatively so identified.
The only thing the anonymous compiler of the pamphlet tells us about Percival (also spelled Perceval and Persival) is that he has heard that "the professional character of Mr. Persival, rises far above the level of mediocrity." Percival's one paragraph opinion on the case says nothing about him; he merely agrees with everything Joseph Aplin has said.
At the time the opinion was written (probably 1801), Spencer Perceval was practicing law in England, probably as solicitor general. He was solicitor general of England from 1801 to 1802, then attorney general (180206), chancellor of the exchequer (180709), and finally prime minister from 1809 to 1812.
Spencer Perceval was the son of the Earl of Egmont. He was educated at Harrow and Trinity College Cambridge, and became a barrister in 1786. He was elected to the House of Commons in 1796, a seat he held for the rest of his life. Perceval was a staunch Anglican; he was outspokenly anti-Catholic, opposing any concessions to the British Catholics, particularly the Irish. His views were generally conservative, but he supported the anti-slavery campaign led by abolitionist William Wilberforce. George III appointed him as Prime Minister in October of 1809, a post he held until his death in 1812. Perceval has the distinction of being the only British Prime Minister to have been assassinated; he was shot in the lobby of the House of Commons by John Bellingham, a deranged man who had been trying to get compensation from the British government for financial losses.
The question remains, if "Mr. Percival" is actually Spencer Perceval, why would a supporter of the abolition of slavery be willing to give an opinion on the case of DeLancey vs. Woodin? And why would he agree with Joseph Aplin's opinion that trover was the correct action in the case? The answer may be that as a lawyer Perceval felt obligated to report his understanding of the law as it was at the time, despite his personal opinion on the subject of slavery in general.