this surname crops up greatly in my researches in the 1600's/1700's in Rushton Spencer and Horton parishes outside Leek - there are plenty in that town also. As most surnames were generally given in a major tax attempt c.1327 A.D. They were based on the nearest little locality etc. unless you already had a well known trade, especially in a town. There is a 1557 reference to an area Turnock, next to Siddington in Prestbury parish in Cheshire. I assume this is the origin of Turnocks. However, there is also a Turnock mentioned in an old deed , near Cheddar in Somerset.
In 1605 and 1606 Thomas Turnock of Heaton, next to Rushton Spencer, buys land from Edward Hollinshed of Heywood, Cheshire. By 1622 this Thomas seems to have moved to Ratcliffe, Lancashire. However, most of the Turnocks of the Leek area seem to be connected to him or richard T. , mentioned in 1617.
Hope this is useful.