Plurals are usually a straight 's' without the apostrophe. So Cockneys, shoes, etc. You'd use an apostrophe as another way of saying 'is' , so 'The cockney is getting a bit annoyed' could also be written as 'The cockney's getting a bit annoyed'. Or 'this shoe's too tight'.
Another reason to use an apostrophe is, as you say, when it's used in a possessive way (e.g. the cockney's shoes, which is another and more elegant way of writing 'the cockney; his shoes'.
When its a plural (i.e. we're talking about the shoes of more than one cockney, the apostrophe comes after the plural, so it would be 'the cockneys' shoes', which is the combination of plural and possessive.