In 1711 George Trosse, who had paid for his schooling, died and left Mudge half of his library, including a number of Hebrew works.

In 1759, after the last mason's work had been completed on the Eddystone Lighthouse, and Laus Deo cut on the last stone set over the door of the lantern, John Smeaton conducted Mudge, his old friend, to the top.

He was buried by the communion table of St. Andrew's, Plymouth, and his funeral sermon was preached by John Gandy, his curate for many years, who succeeded to the vicarage.

Johnson drew Mudge's character in the London Chronicle for 2 June and wrote: Though studious he was popular, though argumentative he was modest, though inflexible he was candid, and though metaphysical he was orthodox.Mudge harmonised well with the unemotional form of religion that was dominant in his day.

James Boswell wrote that he was idolised in the West of England, and sermons were greatly esteemed for fifty years after his death, particularly as suitable for Oxford students.

Another, separately published in 1731, was entitled ‘Liberty: a Sermon preached in the Cathedral Church of St. Peter, Exon, on Thursday, 16 September 1731, before the Gentlemen educated in the Free School at Exeter under the Rev.