Ham and piccalilli is the ham sandwich answered with a relish, and the relish is the whole reason it has its own name. Piccalilli is a mustard-and-turmeric pickle, bright yellow, sharp, gritty with mustard and studded with cauliflower, onion, and other diced vegetables held in a thick spiced sauce. Against cooked ham it does three things at once that a plain ham sandwich cannot do for itself: it cuts the salt and fat with vinegar, it lays a hard mustard heat over the meat, and it puts crunch into a filling that has none. The defining fact of this sandwich is that the variable component is loud. Where the bare ham sandwich is decided by restraint, this one is decided by how a strident relish is held in proportion so it seasons the ham rather than burying it.
The craft is the stripe and the seal. Piccalilli is wet, acidic, and assertive, so it is applied as a measured band down the ham rather than spread wall to wall, because a flood of it soaks the crumb and tips the sandwich from sharp to sour. Butter on the bread is structural here as a barrier as much as a flavour: it waterproofs the soft crumb against the relish's vinegar so the bread holds its body until the sandwich is eaten. The ham goes in at a thickness that can stand up to the mustard rather than vanish under it, and the bread stays soft and plain so the only crunch in the build is the cauliflower and onion suspended in the pickle, which is exactly the textural job the relish was brought in to do. Balanced correctly, the sandwich reads as ham given an edge; tipped too far, it reads as piccalilli that happens to contain meat.
The variations are the other ways the British counter sharpens a ham sandwich, each earning its name from the agent it uses. Ham and mustard takes the heat without the vegetable crunch; ham and pickle swaps the mustard tang for Branston's sweet-sour fruit; ham and tomato reaches for moisture instead of acid. Piccalilli itself runs from a fine, smooth, hot-mustard style to a chunkier, sweeter, more vegetable-heavy one, which changes the same sandwich without changing its logic. Each deserves its own article rather than being crowded in here.