In 1776, he was contracted to design and build Polesworth Bridge over the Coventry Canal at Polesworth, for which he was paid £364. In 1780, he was also contracted to build and design Duke's Bridge in Coleshill, for which he was paid £306.
Although his date of birth is unknown, it is known that Thomas Sheasby was christened on 28 October 1740 in Tamworth, Staffordshire. He was later described as a builder from Tamworth who carried out repairs to bridges for the Warwickshire Quarter Sessions between 1775 and 1787.