I am a vet, and have been to lectures on this. So although 'purebred' fertile cats of any of the ex-pet big cats are very unlikely, interbreeding with each or Scottish wildcats or even an adventurous domestic tom are probably not that uncommon, and most sightings are probably of these sterile crossbreeds hence being often 'labrador sized'. They can also live 15-20 years with no natural enemies in the wild, and would only need to encounter their own species once in 15 years to keep the population going, added to which there are still illegal pet trades where animals can be purchased on the black market, and these probably get released whenever the owner gets fed up and/or fears discovery. Also there have been escapes from zoos and reserves (if domestic cats can escape from any pet carrier designed to man, I bet escapes are a lot more common than reported). In 2022 DNA was found confirming the presence of big cats in the UK:

https://www.discoverwildlife.com/news/new-dna-evidence-confirms-presence-of-big-cats-in-the-uk

And there have been many many sightings and video recordings. Have a look at the puma watch website 😁

(It's only really famers of sheep and birds that have to worry as they are extremely introverted and will stay away from humans as much as possible. At least I hope it stays that way!)