I was surprised and intrigued to read this. I had no idea there was anywhere that did not have pike. But a quick Google found the following statements, although not from definitive sources:
"With the exception of Cornwall, pike are fairly well distributed throughout the country." (fishing.co.uk)
"Found in most parts of the U.K. except northern Scotland, parts of Cornwall and west Wales." (uksafari.com)
"In the UK, pike can be found in every county of England, except Cornwall..." (norfolkfishing.com)
The West Country is riddled with rivers, I don't see why Pike would not have spread througout the region, as they did in the rest of the UK. They are known to have been in the UK for at least 500 million years, so there has been plenty of time for pike to spread to the West Country. Is the climate really too mild to support pike? And if that's so, why are the pike in this pond thriving?
(According to norfolkfishing.com, chub are also not found in cornwall)