I think of the core of the East End as being Tower Hamlets and Newham, and perhaps Barking and Dagenham as well. Streching outwards would include Ilford, Greenwich, Bexley, Lewisham, Hackney, Islington, Waltham Forest etc.
Politically, the East End has had concentrations of fascism (a BNP councillor in the Isle of Dogs in 1993), communism (a Communist MP in Stepney in 1945), anti-fascism (the Battle of Cable Strret 1936), and high populations of immigrants / Jews/ Asians at different times.
I suppose the proper answer is that there is no definite boundary, it's just a cultural / traditional thing.