It was easily for some years, but now the breeding of Giant Otters has kickstarted its sister park in the New Forest also has the same four. I don't think any other UK zoo reaches above two species - though several do have two (Chester, South Lakes and Colchester spring to mind).
Both parks are heavily biased towards otters and owls - Chestnut was the original park and has only about half-a-dozen species other than the 'two Os'; New Forest started out as a general UK wildlife centre and even after being acquired by the owners of Chestnut (the Heap family) has stayed a lot more varied. The same owners also now own Battersea Park Children's Zoo in London - which has a paltry one species of otter!
The centres are both missing one species of otter found in UK zoos - the Smooth-coated. Two other species are in Europe but only found at a single collection each - Northern Sea Otter and Spot-necked Otter.
Chestnut's Giants were the only ones in the UK for many years and Chestnut is currently the only particularly interesting animal collection in my home county of Derbyshire (though thankfully there are several not too far over its borders!).
2010 litter: 2.1 born, 2.0 survived - both these males now at New Forest
2011 - 1.1 surviving, the male from this litter was later transfered to New Forest and then on to a collection in Trinidad recently - which has left 1.2 at Chestnut and 2.0 at New Forest
A female cub was also born last year and reached several weeks before dying suddenly