The magazine 'Fortean Times' does a Big Cat roundup every year, correlating all the sightings, there do seem to be rather a lot, and from right across the British Isles. I can't believe there could be so many ABC's keeping their heads down (for the most part) in our countryside, but some of the kill evidence on some livestock, and I think even the odd deer do have some scientists convinced of Big Cat predation. Also, many Big Cat's are nocturnal predators - hunt at night, lie up somewhere quiet during the day.
I think it's very possible we have a few here and there in the remoter parts. If there are, how they got here would be an interesting question.

I think that a lot of sightings are just people getting carried away when they see something move out of the corner of their eye or when it is getting dark because there seem to be so many sightings they can't all be true. I know several people who claim to have seen a big cat in Surrey, and I remain very sceptical that they have even though it is possible.