Afraid I can't add anything authoritative on what is responsible but the discussions are intriguing. Whether there are big cats wild in the UK or not will likely run and run, but if there are they would have most likely have come from exotics kept as pets that were released by their owners, rather than take the alternative options, when the Dangerous Wild Animals Act came in in 1976. That was nearly 40 years ago - probably at least 3 generations of these species later. That means either continued releases, which seems unlikely, or sustained breeding, which also lengthens the odds.
Anyway, putting that aside... Big cats will eat in situ if they don't feel vulnerable. Lions are the obvious example, but I seriously doubt a roaming pride of lions!!!
However I have seen examples of leopards quite bold enough to eat in the open and sometimes in daylight where they are the dominant predator in that system (as they certainly would be over here). Whilst normally lions and spotted hyena would "outrank" them, where these are absent (for example on African farm land due to eradication) the leopard will be top dog, so to speak. Kills can then be left in the open with no attempt to disguise or cache them. The broken neck is actually typical of a leopard but the pattern of missing tissue isn't. The "cleanness" of the area stripped of flesh and lack of marks on the bones is really odd too for any predator.
If there are big cats wild in the UK they are most likely to be one of the solitary types, e.g. leopard or puma (mountain lion/cougar - although recent data suggests these could be more social than previously thought). They are exceptionally stealthy and will not necessarily run. There are many examples showing how well camouflaged these creatures can be and if they believe they haven't been seen they will stay put. A human may need to get exceptionally close to make them bolt (within 5m for example) although I would agree if dogs had the scent this would be a different situation. They are also stealthy enough to approach people and other animals with them having no idea whatsoever of their presence. Leopards are frequently known to sneak up on large dogs (think alsatian size) on African steadings and spirit them away without a sound being heard and even to take dogs from within houses at night.
I guess what may be worth doing would be to survey the area moving outwards in ever widening circles looking for other signs - be they fur, tracks, disturbed ground, blood trails and so on. Given the strange behaviour towards the road boundary I'd do the same all along there, especially looking at any gaps where a predator could have hidden or come through. We also shouldn't ignore the human angle. I think you said this was a friendly sheep so it could have approached a human interloper in the field. Horns give leverage to break necks and tissue can be cleanly removed with a knife - although quite why like this would be anyone's guess. Are there any signs of other people on site - footprints etc, tyre marks on the grass verge etc?
Hope you get some answers.