How common are raccoons? They are a very common species but Drayton Manor is the only place I know that has them.
Pretty damn common, all things considered - among the places with them are Yorkshire Wildlife Park, Bristol, Gentleshaws, Hamerton and Shepreth to name but a few.
Newquay is looking like my best bet to get a lot of what I want. Pity it's five hours away by rail.
Truth be told, it might be best were you to stay in Newton Abbot or somewhere similar, much as I did last year - this way you will be within a train commute of Newquay, Exmoor, Axe Valley, Paignton and Shaldon, all of which contain some of the unusual carnivores you seek.
Those Bristol ones are show animals-that's why they are set back and less 'on show'. I am trying to remember what they had when I last went-definitely raccoons & civets, I think coati possibly not sure about genet. Of those only the raccoons were regularly in the shows, the others being more recent arrivals that were being trained up (this was late last summer-2013, so could have changed).
Having never seen a common palm civet, I was rather kicking myself when I learned these enclosures had the species shortly after Zoohistorica, as I always disregard these enclosures