My money is on the Otter.
As I'm interested in this SparkleySarah and I'm not trying to be funny, why don't you think it is Otter predation?
I have been involved in several cases where Koi and other carp have been predated by Otter in South Lakes and can say that there is no regular pattern to where an Otter starts to eat a large fish like a carp.
I've a number of images of carp to 18 lbs that have been killed and partly eaten. On one fishery, nearly all the fish found partly eaten had been eaten around the vent and stomach areas. One, possibly two Otters did this and only ceased when nearly all the large carp had been killed and ironically, one Otter was killed on the road close to the fishery.
One local angling club has lost over £20 000 worth of carp to Otter and has now installed an Otter proof fence around one of its fisheries (I've put pics in My Images of this).
Secondary consumption may also be possible. Scenario - Otter removes carp from pond and partly eats it nearby. Fox, mink, rats and birds (and Hedgehogs - yes, they're still around) either move or continue to graze on the carcass. I have personal experience of a mink dragging the carcass of a 12 lb Salmon 15m and pulling down a small hole under a slab of concrete. The only way I found the fish was that it had been radio tagged.
Autumn into the early winter appears to be the favoured time for carp predation possibly due to the cooler water induced lethargy. An Otter has been observed catching a decent sized carp from a static pod without disturbing the rest of the fish. It is pretty much guaranteed that the Otter will return until the food source is depleted.
The other clue is in the location of the carcass. The reason it is so far away from the pond can only be speculated on. There may well be cubs to feed at a distant holt. As Otters can produce young at any time of year and from recent reports of a bitch and two cubs in the Carlisle area, it is possible that it was being taken back to the natal holt.
If it were for individual consumption, it would normally be eaten on site, often under cover of convenient shrubbery if present.
A good scaled image of the spraint / scat would be interesting.
This has brightened up a very wet Cumbrian morning.