A correct answer exists, which is good because this is a very ambiguous question.
The big problem is that the length of a coastline can't be precisely calculated. Whatever scale of map you choose to use, zoom in further and the length of the coastline inexorably increases. What looks like a bay may include several coves, and they in turn may have rocks jutting out into the sea with complex irregular surfaces, and just what height did you think the tide was at anyway? Indeed when mathematician Benoit Mandelbrot wanted to popularise the concept of fractals in the 1960s he chose to call his paper "How long is the coast of Britain?"
"Seacoast shapes are examples of highly involved curves with the property that - in a statistical sense - each portion can be considered a reduced-scale image of the whole. The concept of ‘length’ is usually meaningless for geographical curves."
It all comes down to how many points you choose to measure between. For example if your map of the British coastline has 2282 vertices then its length would be 3876 miles, but if you increase the number of vertices to 2,282,000 then the length shoots up to 11,023 miles. Alasdair Rae's written an excellent post explaining how the calculations work, with diminishing gifs, if this piques your interest.
But to find the longest coastline only requires putting the English counties in order, not calculating absolute values, so I only need to be consistent in my measurements. Here's what happened when I tried measuring the coastline of (ceremonial) English counties using Google Maps.
1
Cornwall
410 km
2
Devon
340 km
3
Kent
270 km
4
Essex
260 km
5
Cumbria
220 km
By my calculations the longest coastlines belong to Cornwall and Devon, two southwestern counties with the sea on both sides. Kent is surrounded on three sides, but is a smaller county, while Essex's high showing is due to its high number of creeks and estuaries. But don't read too much into these rankings because I was only using Google Maps level 9, and zooming into level 11 changes the order somewhat.
1
Cornwall
460 km
2
Devon
390 km
3
Essex
320 km
4
Kent
280 km
5
Cumbria
230 km
Cornwall, Devon and Essex have each put on about 50km, or 15%, because zooming in has revealed a lot more coastal contortions. Meanwhile Kent and Cumbria are only up by 10km, or 5%, because their coastlines are less indented. Bays and cliffs don't increase in length as you zoom in as much as creeks and estuaries... and this has allowed Essex to leapfrog Kent.
I could zoom in further and calculate again, but that's not a great use of my time. Instead let me switch to a potentially more accurate measurement courtesy of GB circumnavigator Quintin Lake. He's just finished five years of walking round the British coast, sticking as close to it as possible and taking some gloriousphotographs along the way. He's also kept very careful record of kilometrestravelled and produced a summary map, which has allowed me to compile this Top 10 of County Coastlines.
1
Cornwall
724 km
2
Essex
526 km
3
Devon
509 km
4
Cumbria
352 km
5
Kent
321 km
6
Lincs
238 km
7
Suffolk
234 km
8
Norfolk
232 km
9
Dorset
222 km
10
Sussex
219 km
This won't be perfect either because rights of way don't always follow the coast, but because it's micro-level data it's likely much more accurate than my blunt Google Maps estimate. Notice that the distances are a lot higher than before, as you'd expect from finer detail, with Cornwall and Essex receiving a particular boost. Quintin found walking around Essex somewhat tortuous, forever following another sea wall up another inlet, which has leapfrogged this unassuming county into second place. Even better, this turns out to be correct....
Three years ago the Ordnance Survey bashed the figures by measuring the length of the High Water mark on a 1:10,000 map. They only published a top three, annoyingly, but as the ultimate arbiters of all things map-based their top three ought to be correct.
1
Cornwall
1086 km
2
Essex
905 km
3
Devon
819 km
Devon is confirmed in third place thanks to its twin shores, and Essex's estuarine wiggles place it comfortably in second. But the English county with the longest coastline is definitely Cornwall, because it turns out you can answer the question even when you can't measure the data.