From Longman Dictionary of Contemporary Englishaitchaitch /eɪtʃ/ noun (plural aitches) [countable, uncountable] the letter H when written as a word not a letterdrop your aitches (=not pronounce the letter H at the beginning of words) People with Cockney accents tend to drop their aitches.
Examples from the Corpus
aitch• Not only are aitches dropped, appalling vocals now reign virtually supreme in the realm of pronunciation.• Some foreign learners also have trouble with their aitches.drop your aitches• Instead, he drops heavy hints.Jeffrey Archer drops names like some people drop their aitches. 