Acherley was probably the first person who, in 1712, advised the moving of the writ for bringing over the electoral prince, afterward George II, to take his place in the House of Lords as Duke of Cambridge; but the intrigues in which he indulged for the furtherance of this object were cut short by the death of Queen Anne on 1 August 1714.
Thereafter he pressed Barons Leibnitz and Bothmer for professional advancement in recognition of his admitted services to the house of Hanover.
Acherley's reputation rests upon his political, legal, and constitutional treatises, which have now, by lapse of time and the development of methods, been largely superseded.
He added an Appendix containing several original Letters and Papers which passed between the Court of Hanover and a gentleman at London, in the years 1713 and 1714, touching the right of the Duke of Cambridge to reside in England and sit in Parliament.
Acherley is also credited with the authorship of an anonymous pamphlet of forty-six pages, called The Jurisdiction of the Chancery as a Court of Equity researched, 8vo, London (1733), third edition (1736).