I hope you would not mind being helped by a French native. Anyway I checked this point out . The place of adverbs such as never, rarely, often... and generally speaking the adjuncts of frequency are expected just between the auxiliary verb and the main verb:
He should never have answered the question.
However, never can be placed before the verb group in order to emphasize the negative statement.
He never should have anwered the question
There never have been any plot
Both structures are grammatically received if I may say so.
If in doubt, replace the word with something close and see it if still makes sense. The use of NEVER is questionable here when you actually mean NOT in the context of the sentence. so....
I should not have allowed you....this sounds ok, so you can substitute NEVER instead of NOT to give more emphasis to give the meaning of 'under no circumstances' as opposed to 'under this specific circumstance'
I not should have allowed you....this is clearly not very good so any substitution of a more emphatic word like NEVER is still going to be not very good. (Notice I didn't say it is incorrect, your style is yours, it is up to everyone else to decide whether it becomes common usage).
The use of 'never should have' is quite common in American English. My guess is that it is not at all unusual in BE either.
Here is an example from the Cambridge Dictionary:
. "He threatened to shoot, but I never thought (= did not think) he would." Cambridge Dictionaries Online - Cambridge University Press
If we followed your logic strictly, then in the sentence from Cambridge we should be able to say "...I not thought he would." But, of course, we can't.
Google produces nearly a million results for "never should have" and the BNC also offers some examples of the same wording.
I'd say yes, but probably somewhat less frequently, Dihen. The primary reason for 'never' being used either before or after 'should have' (or 'would have' or 'could have') is probably that 'should have' is contracted spoken English (should've, would've, could've).
I agree. The placement of the word never has some flexibility here. But the end of your sentence (when I had the chance) is quite awkward in combination with the beginning.
You can even say 'I should never have...'; I imagine some prescriptive grammars might even have preferred it once (as it doesn't split the auxiliary from the participle - and, as we all know, prescriptive grammars have a horror of splitting anything ).
I think what makes 'when I had the chance' awkward is that that expression tends to follow a positive regret: 'I should have done [whatever]when I had the chance'.