After serving for a time as chaplain to Bishop Simon Patrick, he was presented on 10 March 1698–9 to the living of Rattenden in Essex, which he exchanged in the following June for a chaplainship at Chelsea Hospital.
On 3 July 1701 he was collated to a prebendal stall in Ely Cathedral, and was elected on the next day to the mastership of Jesus College, Cambridge, both offices being vacant by the death of William Saywell.
He contributed to Joseph Wasse's Bibliotheca Literaria, 1724, an article, "Tully and Hirtius reconciled as to the time of Caesar's going to the African war"; also an emendation of a passage of Justin Martyr.
William Reading's editions of Origen's De Oratione (1728) and Historiæ Ecclesiasticæ Scriptores (1746) are said to have been in great part the work of Ashton.
p. 80), it was Ashton's edition of Hierocles of Alexandria's commentary on The golden verses of Pythagoras that was published as by "R. W." (i.e. Richard Warren).