Ibbetson was probably educated in a local Moravian community at Fulneck and then by Quakers in Leeds. Between 1772 and 1777 he was apprenticed to John Fletcher, a ship painter in Hull where he also enjoyed some success as a theatrical scene painter for the Hull Theatre.
In 1777 he moved to London, where for the next decade he worked as a picture restorer. From this employment he was able to acquire a thorough acquaintance with the works and methods of Dutch artists.
In 1785 he exhibited at the Royal Academy A View of Northfleet, and continued to exhibit during succeeding years. Through the connoisseur Captain William Baillie, Ibbetson was appointed draughtsman to Colonel Charles Cathcart on the first British embassy to Peking (Beijing) in 1787. Cathcart, however, died at Java during the voyage. Ibbetson returned to England, having made many drawings of the fauna and the scenery encountered during the voyage that included visits to Madeira, the Cape of Good Hope and Java. He was also able to obtain nautical experience which he afterwards turned to account in his pictures.
In 1789, Ibbetson went to visit Viscount Mountstuart at Cardiff Castle. This was the start of a long association with Wales, where he painted numerous scenes of folk life and picturesque scenery as well as detailed watercolours of iron furnaces, coal staithes and copper mines, which provide an important record of early industrial developments in that part of the country. A visit to the Isle of Wight in 1790 was the inspiration for a series of paintings of shipwrecks and smugglers.
The death of his wife in 1794 and sole responsibility for three small children, together with financial difficulties, brought on an attack of brain fever from which he recovered to find that he had been robbed of all his possessions by his servants. In 1798 he left London and moved to Liverpool to escape his creditors. From there he moved to Ambleside where in 1801 he married his second wife, Bella Thompson. He was also resident for a while in Edinburgh.
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