The Parson Russell Terrier is recognised by the Kennel Club (they were oroginally called Parson Jack RussellTerriers, but the 'Jack' was dropped so they did not become confused with what we all know as Jack Russells, i.e. the shorter legged hunt terriers. Have a look at the breed standard for the Parson Russell:
http://www.thekennelclub.org.uk/item/82
There is also a registry used by many European/foreign countries called the FCI which is their equivalent of the Kennel Club, and they also register the Jack Russell Terrier, which is based on an Australian standard, but stems originally from the smaller 'hunt terriers' from the UK
http://www.dogdomain.com/FCI/fcistandards/fci- 345.htm
There are also clubs in this country which keep records of Jack Russell Terrier pedigrees, but they are not a KC recognised breed, although they do breed them pure.