Whitechapel to Limehouse is the east-end walk that stays genuinely east. Four and a half kilometres of streets that still remember being working docks, with a Victorian music hall, a 1978 political mural, and a 250-year-old pub at the end.
Start at the Whitechapel Gallery, not the market. Five minutes south you hit Cable Street, and within ten more you're at the mural — the 1978 artwork commemorating the anti-fascist Battle of Cable Street of 1936. It is genuinely large and genuinely moving.
Wilton's Music Hall is a few minutes further east. It's the oldest surviving grand music hall in the world, somehow still operating, and even the exterior is worth circling. If the Mahogany Bar is open, have a drink in it; there is nothing like it.
East through Shadwell Basin — an old dock converted into housing in the eighties — and you come out at Limehouse Basin. The walk ends with narrowboats, modern glass, and, if you want to add a detour, the Grapes on Narrow Street — an actual 500-year-old riverside pub.