Which English county possesses the greatest amount of coastline?

If you mean English counties, although I've seen a couple of references to Essex as the longest, I tend to believe it is Cornwall: http://www.cornwall.gov.uk/leisure-and-culture/beaches-in-cornwall/

Talking about the historical counties of England I think Cornwall is right.
Its coast is said to be 476,6 km.

However, another site says that Devon has a coast of 433 km at Mean Low Water and 695 km at Mean High Water. Could anyone explain that?

The answer to author's question is that presumably as the tide goes out, it uncovers all those meandering "fronds" in estuaries and mudflats which add immensely to the coastline.
This has the opposite result on the county's area, as shown by the trick question, which is the smallest English county by area, which I think I'll submit as a new question.

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Oops! Just realised that the effect I mentioned would have the opposite effect on the coastline, ie at low water it would be longer. Sorry. Perhaps that reference has it wrong.

It would seem to be Cornwall, with 697 km (422 mi) of coastline. Essex, with 563 km (350 mi) comes next.

https://en.wikipedia.org/wiki/Geography_of_Cornwall
http://www.bbc.com/news/magazine-11485792
http://www.breakfreeholidays.co.uk/blog/englands-record-breaking-county-whats-essex-2014/