Dropping the h
The speech habit of not pronouncing the letter 'h' where it is pronounced in RP is called dropping the h. It is widely, and stereotypically, regarded as a mark of the uneducated. It was commonly used in fiction - it still is common, though less so - to represent the speech of criminals, the poor, the uneducated and others by writing 'e, 'im and 'er for he, him and her. In the musical My Fair Lady, Eliza Doolittle, the poor flower-girl being trained to 'talk like a Duchess', sings 'In Hertford, Hereford and Hampshire, hurricanes hardly ever happen' in order to show that she can (now) pronounce her 'h's. In her native cockney accent, she says 'In 'ertford, 'ereford and 'ampshire 'urricanes 'ardly ever 'appen' - to the disdain of the educated gentlemen around her.
Oddly, the so-called dropping of 'h's has a reverse side. There is a form of adding the 'h', although it is rarely named. It used to be normal in the fictional portrayal of cockney to allege that the Cockney speaker not only drops the 'h' from words where RP has it, but puts it in where RP does not. 'Hin the Hisland' might be such a representation of a Cockney saying 'in the island'. AWE is not sure that this is very noticeable in twenty-first century Cockney.
For a form of dropping the h that was prestigious, rather than denigratory, see H with indefinite article.