Cook the beetroot in a saucepan of boiling water for 30–60 minutes, depending on their size, or until a knife can be inserted into the largest one easily. Drain, leave to cool, then peel off the skins with a small knife.
Meanwhile, pour the vinegar into a saucepan, add the sugar and remaining ingredients. Heat gently, stirring from time to time, until the sugar has dissolved. Increase the heat and simmer for 3 minutes, then remove from the heat and leave to cool.
Cut the beetroot into chunks and pack into warm, dry jars. Pour over the cold vinegar mixture to cover the beetroot completely and so that the vinegar comes to the top of the jars (adding a little extra vinegar if needed). Screw on lids, label and leave to mature in a cool, dark place for 3–4 weeks.
To serve, try tossing some mixed lettuce leaves in a crème fraîche dressing, then top with flakes of peppered smoked mackerel and spoonfuls of drained beetroot with just a little of the vinegar mixture.