I have found three written sources for the pronunciation of Calne:
Canon Jackson wrote a history of Calne in 1888 and writes: "We pronounce it now Calne (Carn)"[1]
The Pronunciation of 10,000 Proper Names (1909) one states that it is "kôn", where 'ô'would be said as 'ôr'. This is where I start to wing it and suggest that this phonetic would lead to a pronunciation of 'Kon'.
The Place-Names of Wiltshire (1939) states that it uses local pronunciation and provide Calne as "Kɑːn, vulgo Kan" (modern phonetic symbol used. vulgo translates to 'generally'). The 'ɑː' said as in 'father', which makes this 'Kahn' This does seem a little closer to one of the local pronunciations.
Both books are from the last century, with one being over 100 years old. So here are the three pronunciations that I have come across (with my attempt to type them the way I hear them):
Karn
Caln
Calen (this one is less used in the UK, although I have heard it used more than once. It is the way that our friends over in Caln Township pronounce their town name).
I've found it quite difficult to separate the two main pronunications (Karn and Caln) and the people who use them. I've spoken to different people and seen debates online - both sides say they've had families that have lived here for generations.
I find it interesting that in places like this, where there are different ways of saying the same word, people become very entrenched in their pronunciation being the correct one. I guess it must feel like part of their identity? I know I feel a bit like that with my surname!
I've been in rooms where people are conversating and pronounce Calne differently, but nobody flutters an eyelid. If everyone recognises the word being said, then does the pronunciation really matter? I think that's the way to approach it as language is less prescriptive than it was and changes evolve and spread quicker than ever before. There must have been a time when the town was pronounced a single way, but then diverged? Perhaps with an influx of newcomers at some point in the past.
At the end of the day, there is no 'official' way to pronounce Calne - as much as we'd all like our way to be 'the' way. So as long as we understand which town we're speaking of, then I personally think that's the main thing.
Sources:
[1] Jackson, J., 1853. Calne. The Wiltshire Archaeological and Natural History Magazine, XXIV, 166-219.
Gover, J., Mawer, A. and Stenton, F. (1970). The place-names of Wiltshire. Cambridge: At the University Press.
Mackey, Mary Stuart; Mackey, Maryette Goodwin (1909). The pronunciation of 10,000 proper names. New York: Dodd, Mead and Company.
