A lot of Cockney rhyming slang is used here in Portsmouth & weirdly the Portsmouth accent sounds very much like a Cockney accent too (unlike the rest of Hampshire which has more of a country bumpkin slant). Apparently it's thought that the reason is that years & years back many dockyard workers were brought down from the EastEnd to work down here & I guess all their families moved down too... Very strange!
Yeah a hell of a lot of Cockneys also moved out of London after the War. They'd lived in the parts of London worst hit by bombing, and lots had been working for the war effort outside of London during the war and grew to like it. Portsmouth's wartime Cockney Dockers are a good example of that.
All those towns and cities along the south and south east coast of England recieved a huge influx of Cockneys in the 50's, 60's and even into the 70's, in part because those were towns Cockneys had traditionally gone on their summer holidays to. Brighton is a really good example, partly because it's so close to London, its population exploded after the war with Cockneys escaping bombed out slums. The old Brighton accent basically disappeared, and was replaced by a kind of Cockney-esque London-ish accent.
Just FYI, and I know this will be controversial among people from the East End of London, but not all Eastenders are Cockneys, in fact the real heartland of the Cockneys is in Southwark (in the Borough, Bermondsey, Waterloo and London Bridge) south of the river (whereas the East End is generally thought of as north of the river) the area thought of today as Cockney in the East End is far larger than it was historically. Essentially the test of your Cockneyness is whether or not you or your family come from an area in which you can hear Bow Bells (the bells of the Church of St Mary-le-Bow). That includes parts of London south of the river, and excludes certain parts of the East End.