One of my readers told me about this months ago (sorry I forget who) but I finally got around to visiting.
It certainly looks like a stench pipe, although its location is a little unusual as most of them tend to be either in built-up areas or near grand houses. This one stands in a relatively rural location at the edge of Great Ayton.
Great Ayton Stench Pipe
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Assuming the location is Station road, it is a stench pipe, Great Ayton has had a sewage system for a long time, the first treatment works was built in 1898. The sewer system has been researched by a local group.