Now I come to think of it, you need your vertical aperture not to be in Cornwall but the tropics to do the calculation. (In his case it was in Syene, where he knew the sun shone down a well at midday at Solstice). http://www.juliantrubin.com/bigten/eratosthenes.html

So the short answer is no, a vertical aperture in Cornwall wouldn't help. ;) Sorry!