A 'Mockney' is a mock-cockney - a person that exaggerates a coarse London accent and uses dialect words in a self-conscious way. Personally, I thought Jamie Oliver was not even a mockney but a Faux Essex-Boy. It is inverse snobbery, but needs to be done with conviction to avoid looking condescending.

See also this website.

Some people think it's called Estuary English because many upwardly mobile professional people among whom it is fashionable live in the Docklands area of London by the river. [Actually, it's called estuary English because it is spoken in the estuary of London, which takes in a larger area than just the docklands.] It is also called Mockney because it is a fake or MOCK form of Cockney English, without all the colourful language play and complex use of slang that make Cockney English so fascinating.