There is no definitive answer. It depends on the scale on which you measure it. The smaller you choose the unit of measurement to be, the longer the coastline. If you use a meter rule, you get one value. If you use a matchstick, you get a different result. And this might also change which of two counties has a longer coastline. i.e. a more rugged coast will gain length more rapidly as the unit of measurement decreases. The extreme of this fact is represented by the Koch Island. The Koch Island is a finite area with an infinitely long coastline.
It probably depends how you measure it, all the inlets, estuaries etc., but I read Cornwall's coastline is 422 miles long and Essex is only around 350 miles. I don't want to spoil the thread, but I am curious... Which county's women have the largest waistline? Norfolk?
LOL, Rutland is landlocked, used to be part of the beautiful East Midland County of Leicestershire, now back as a county in its own right, and is the smallest in England I believe... lovely part of the world, and very much underated IMO.
However, back to the original question, I thought Cornwall would have the longest coastline too..