Perhaps, but unconfirmed.
There have been numerous reports of a "beast of Bodmin/Dart moor". There is a list of reports of contacts with big cats here thanks to Weather Vane. The best evidence is blurry photos that seem to indicate there is a large cat, but certainly do not allow one to definitively confirm that they are leopards and pumas, or that they are breeding.
The Telegraph reported in 2016 that they had 'solved' the mystery and traced it back to the release of three pumas in 1978 by Mary Chipperfield, the famous circus owner, after her zoo in Plymouth was forced to shut down. If this is the source, then recent sighting would be evidence that there is a breeding population, as the life expectancy of pumas in the wild is 8 - 13 years with a maximum of 20 years in captivity. However, others discount the story: Roger Cawley, the husband of the late Ms Chipperfield, said: "We had no dealings with the old Dartmoor Wildlife Park all those years ago and certainly never released pumas or any other wild animals on Dartmoor."
Example blurry photo:
This is a still from a video reported by the BBC to show a three-and-a-half foot animal.