Pronunciation as 'haitch' would seem London Cockney to us....
Cockney speech is very carefully tailored for the current audience. When a Cockney is speaking to a Non-Cockney he will exaggerate pronunciation and deliberately mis-pronounce words of three or more syllables, especially if there is a similar word which he can use instead.

When talking seriously among friends the accent is considerable reduced. So, a Cockney would usually say 'aitch'. 'Haitch' would be used if a comic effect were intended or for a Non-Cockney audience.

TTFN.