I gave a talk at the Royal Over-Seas League this evening (Over-Seas is always spelt with a hyphen for some reason in the title of the organisation) and there were lots of questions after the talk, one of which was "What exactly is Estuary English?"
I do not speak Estuary English, as I am a northerner, so all my information comes from articles and websites (eg this BBC page). Estuary English is an accent somewhere between RP (received pronunciation) and Cockney, and is popular with many people, as it is not as 'posh' as RP so appeals to those who wish to hide their upper-class origins, yet it is not perceived to be as working-class as Cockney. Tony Blair is said to have adopted Estuary English to sound more ordinary and more appealing to Joe Public. RP speakers adopt some, but not the most extreme, features of the Cockney accent, and this is what gives them an Estuary English accent. So, RP speakers pronounce t in words (water, daughter, bottle, right etc) and Cockneys don't - they use a glottal stop instead. Speakers of Estuary English drop the t in some positions (usually at the end of words) but keep it in others (eg in the middle of short words). The final l of words (eg bill, feel) is likely to be pronounced like a w by Estuary English speakers.
The term Estuary English was coined in the 1980s by David Rosewarne. Here's an article from English Today which he wrote in 1994. It is a fashionable variety of English and has now spread beyond the south-east of England, both northwards and westwards.