Cockney is mainly spoken in East London. A lot of the words are slang and some are just pronouced differently. If you are able to watch an episode of 'Eastenders', this would help you understand the difference. I'm cockney myself but my accent has lessened due to moving to another City. If you have a 'well-educated' accent, that doesn't necessary mean you are educated!

correct english: water, bath

cockney: woo'ar, barth

wiki:Changing attitudes towards Cockney English
The Cockney accent has long been looked down upon and thought of as inferior by many. In 1909 these attitudes even received an official recognition thanks to the report of The Conference on the Teaching of English in London Elementary Schools issued by the London County Council, where it is stated that "the Cockney mode of speech, with its unpleasant twang, is a modern corruption without legitimate credentials, and is unworthy of being the speech of any person in the capital city of the Empire". On the other hand, however, there started rising at the same time cries in defence of Cockney as, for example the following one: "The London dialect is really, especially on the South side of the Thames, a perfectly legitimate and responsible child of the old kentish tongue, the dialect of London North of the Thames has been shown to be one of the many varieties of the Midland or Mercian dialect, flavoured by the East Anglian variety of the same speech . Since then, the Cockney accent has been more accepted as an alternative form of the English Language rather than an "inferior" one; in the 1950s the only accent to be heard on the BBC (except in entertainment programmes such as Sooty) was RP, whereas nowadays many different accents, including Cockney or ones heavily influenced by it, can be heard on the BBC.