The jellied eel sandwich is defined by a texture almost nothing else in the British sandwich canon offers: cold, set, trembling jelly. Eels are cut into short rounds and cooked in a seasoned, vinegared stock that is naturally rich in gelatine, then left to chill until the whole thing sets to a soft, savoury wobble around the fish. Spooned onto plain white bread and butter, the filling is not a spreadable paste and not a firm slab; it is yielding aspic with pieces of eel suspended in it, eaten cold. That set jelly is the entire identity. A warm version is just stewed eel; what makes this an East End thing is the deliberate cold set and the nerve it takes to put it between bread.
The craft is the set and the acid. The stock has to carry enough natural gelatine to hold a clean wobble without becoming rubbery, and it is sharpened with vinegar and pepper so the jelly reads bright and clean rather than heavy, which is the same job vinegar does on a cockle or a piece of fried fish. The eel is left in generous rounds so there is fish to bite against the give of the jelly, the contrast of firm flesh and soft set being the whole sensory point. The bread is plain soft white and buttered to the edges, and it is doing structural work as much as anything: it is a dry, neutral base that contains a cold, wet, loose filling and gives the hand something solid to hold, with the butter sealing the crumb against the jelly so the slice does not turn to pulp. Chilli vinegar from the bottle on the table is the traditional and only real seasoning added at the point of eating.
The variations stay on the same East End counter and keep the cold-set logic. Stewed eels served hot in their liquor with mash and parsley liquor are the warm relative, a different dish entirely. Cockles and whelks vinegared the same way and put through the same plain-bread treatment are the neighbouring shellfish builds. Each of those deserves its own article rather than being crowded in here.