BBC Discover Wildlife magazine have published an article: Black leopards are quietly thriving in the British countryside, as if it was now settled fact. Well almost. They leave some small amount of wiggle room to disbelieve it.
There was a story recently about some lynx escaping from captivity, and they were very quickly sighted and picked up. That's the general situation of how difficult it is for large cats to hide undetected in the British countryside.
I had a wildlife walk in the Carpathians with a wildlife guide once, about 15 years ago. Those woods contain wolves, bears, lynx, which are very hard to see. But signs of them are everywhere. We started our walk and it was not hard for him to spot wolf footprints and bear footprints quite frequently. We were not in a suitable area for lynx. We went on our own walks elsewhere, and knowing what to look for, we found more footprints, and great piles of bear poo. In Slovakia, I've seen great piles of bear poo in the mountains on many of our walks.
Our land is quite scantily forested, the least forested in Europe. If there are big cats out there, they are eating deer and pooping everywhere. If they breed, they have stay in one locality for a while, and there should be a lot of poop to find. Here in the Chilterns, there's a lot of deer and they are rapidly increasing, which they wouldn't be if they were feeding a local population of big cats. Indeed I sometimes wish we had some lynx to eat them.
When we wanted to know if pine martens were present in areas outside Scotland, people put out camera traps, and now we have quite firm undeniable pictures of pine martens in Devon, North-West Wales, the Welsh borders, etc, as well as finding other clear signs of their presence once we know which localities they frequent. Contrary to what this article implies, it is really hard for a big cats to hide in Britain. If they were here, they would be easy to find, a darn site easier than pine martens.
Entertainingly, they link to this article: Big cat caught on camera most likely a leopard says expert. But when you read it and watch the video, it's quite clear it's a house cat. A classic case of size misjudgment, as another more persuasive expert sets out.
If there were big cats persisting and breeding in the British countryside - excluding the occasional escape or release present for a brief time which certainly happens - they really would much easier to find and demonstrated with much better evidence than this.