I googled this a bit just now because I felt an hallucination and a hallucinaton seemed both somewhat correct. Not saying this is the absolute truth etc, but in British english an hallucination could be correct as it has to do with how people pronounce consonants in specific words. Anyway I'm not a grammar police or native english speaker, I just thought I'd share my findings.
Firstly, there is no such thing as "British English". It's simply "English".
"US English" is necessary as a definition, because it's a derivative = not the original form. Much like "Canadian French". There is no "French French". That would simply be redundant (as the original form does not require definition, only the derivative does), much the same as "British English" is. England is a part of Britain. I am English.
Secondly, no. It is not & cannot be correct. You are supposed to pronounce the "H".
If you pronounce the word as "'allucination", dropping the "h", which most people from my neck of the woods do, then you are simply mispronouncing the word.
Mispronunciation does not equate to a change in the rules of grammar.
Most people that I know will say "Yeah, you must've been 'allucinating, mate.", but they will still pronounce the "H" when they say "You had
a hallucination."
Some will say "You 'ad 'n 'allucination".
People saying it, incorrectly, does not make it correct.
Thirdly, as this is written, how people say it is largely irrelevant, anyway.
In order for "an 'allucination" to be correct in writing, as per common vernacular, it would need to be written that way.
"An hallucination" is not, in any way, shape or form, correct, in writing.
Edit: Also, don't worry about "grammar police" or "grammar Nazi", as some like to throw around.
This term is simply a weak attempt at defence by deflection, by the illiterate.