Roast lamb and redcurrant is the cold lamb sandwich resolved with the jelly instead of the mint, and the redcurrant is the part that defines it. Cold roast lamb is a strong, faintly sweet meat with a fat that firms and waxes as it cools, and where the usual answer to that fat is a sharp green mint sauce, here the lead is a clear, set redcurrant jelly: sweet first, then a clean tart note as it goes, glossing the meat rather than slicing across it. The effect is rounder than mint and built on agreement rather than contrast. The sweetness sits with the natural sweetness in the lamb and the tartness trails behind it to keep the whole thing from going flat. The jelly is not a garnish on a mint sandwich. It is a different decision about how to meet the same meat, and it is the part that tells you which roast you are eating.
The craft is in the cut and the way the jelly behaves. Cold roast lamb is best sliced thin and against the grain, because a thick cold slice is chewy and pushes the waxed fat forward while a thin one stays tender and folds to the loaf. Redcurrant jelly is set rather than wet, which is the structural advantage over mint sauce: it spreads in a thin even layer, glazes the meat, and does not bleed a sour vinegar patch through the crumb, so it can go directly against the bread. The discipline is the quantity. A thick layer turns the sandwich into something closer to a pudding, so it is spread thin and the lamb is allowed to stay the dominant flavour. The bread wants real structure for a dense filling, a sturdy white or a bloomer, with butter to the edges to bridge the salt of the lamb to the wheat and to keep the crumb firm under the meat.
The variations are mostly a question of how the fruit and the herb are balanced. Redcurrant alone keeps it sweet and glossy; redcurrant with a stripe of mint runs the sweet and the sharp together in one bite, which is how the Cumberland-style version treats it; rowan or crab-apple jelly swaps one tart fruit for another with the same set behaviour. The plain cold-lamb slice with no fruit and the standard mint-sauce reading are their own things. Each deserves its own article rather than being crowded in here.