He was educated in Coventry, became a successful merchant, traveled widely throughout Europe and for several years was the financial agent of Charles I.
At the age of eighteen, on the 25th of February 1639, he married Margaret, daughter of Lord Coventry, with whom he and his wife lived at Durham House in the Strand, and at Canonbury House in Islington.
In 1640 Lord Coventry died, and Cooper then lived with his brother-in-law at Dorchester House in Covent Garden.
On the death of Southampton, Ashley was placed on the commission of the treasury, Clifford and William Coventry being his principal colleagues.
He succeeded Sir William Coventry as commissioner for the state treasury in 1669, and in 1673 was appointed a commissioner for the admiralty.