Now then you, not all witnesses
"Experts monitoring deer using thermal imaging cameras spotted the animals on two separate occasions in different parts of the Forest of Dean, Gloucestershire. Commission spokesman Stuart Burgess said the sights had been confirmed by "very experienced" rangers unlikely to mistake deer for big cats."
https://www.independent.co.uk/climate-change/news/reliable-big-cat-sightings-revealed-1229204.html
Then there were the witnesses in Devon back in 2011 who reported see a lynx and were later found to be correct as a lynx named Flaviu had escaped its enclosure and hunted and killed four lambs before it was caught in a humane trap and taken back to Dartmoor Zoo:
https://www.devonlive.com/news/devon-news/details-55-big-cat-sightings-2032199
Then I actually met a Norfolk farmer who was adamant he had seen a lynx cross the road in front of him and he was eventually proven right as a gamekeeper shot the creature and put it in his freezer:
http://news.bbc.co.uk/1/hi/england/norfolk/4830320.stm#:~:text=The picture of the northern,of prey was being investigated.
Not everyone is claiming that there are breeding population of so-called "alien" big cats in Britain, but it is an established fact that witnesses have reported seeing big cats and that has included pumas:
https://www.highlifehighland.com/inverness-museum-and-art-gallery/felicity-the-puma/
And then yet another lynx:
https://www.bristol.ac.uk/news/2013/9321.html
Yes, most of these are escapees but the witnesses didn't know that at the time.