Pour the vinegar into a stainless-steel or enamel saucepan and add the allspice berries, salt and brown sugar. Bring to the boil, then remove the pan from the heat, cover and leave to stand for 2 hours.
Meanwhile, wash the beetroot, taking care not to break the skin. Place it, unpeeled, in a saucepan and add enough water to cover. Bring to the boil, reduce the heat, cover and simmer for 1 1/2 hours, or until it is tender. While the beetroot is cooking, scrub, peel and coarsely grate the horseradish.
When the beetroot is cooked, remove the pan from the heat and leave the beetroot in the water to cool completely. Drain, remove the skin and dice the ﬂesh.
Pack the beetroot and horseradish, in alternate layers, in clean, warm, dry jars. Bring the spiced vinegar to the boil and pour it into the jars to cover the beetroot and horseradish completely. Cover the jars with vinegarproof lids and, when cold, label, date and store in a cool, dry, airy cupboard for one month before using. Use the pickled beetroot within three or four months.