As part of this work, Eastburn surveyed Hatfield Chase in 1776 and produced technical drawings such as that of the winding engine at Walker Colliery in 1783 and Aberdeen Harbour in 1788.

[3] The same year, Eastburn worked with Jessop on a proposal to transport water between the River Colne and Marylebone.

[3] Eastburn then was engaged as resident engineer on the southern Lancaster Canal, between Garstang and Wigan—a position he held until 1798; this work was performed under the supervision of John Rennie.

[5] Eastburn's will was written in December 1812, bequeathing his estate to his wife (or, in the event of her predeceasing him, his then-recently widowed daughter).

His precise date of death is not known, although he was buried at the church of St Maurice, Monkgate in York on 5 July 1821.