In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Aislaby like this:
AISLABY, a chapelry in Whitby parish, N. R. Yorkshire; on the Esk river and the Whitby railway, at Sleights station, 3 miles SW of Whitby. Post Town, Sleights under Whitby. Acres, 1,068. Real property, £1,568. Pop., 330. Houses, 76. A building limestone is quarried here, and was the material of Whitby Abbey and of several great modern works. The living is a p. curacy in the diocese of York. Value, £87. Patron, J Boulby, Esq. Charities, £11.
GB Historical GIS / University of Portsmouth, History of Aislaby, in Scarborough and North Riding | Map and description, A Vision of Britain through Time.
Date accessed: 27th March 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Aislaby ".