Place the beets in a pan of salted water and bring to the boil. Simmer for 30 minutes until cooked, then drain and leave to cool. You should be able to slip off the skins once they're cool enough to handle. Halve or quarter any big ones, leave smaller ones whole.
In a separate pan, add the vinegars and sugar. Halve the chillies lengthways and add to the pan along with a squeeze of lemon juice, the coriander seeds and a pinch of sea salt, then place over a high heat. Bring to the boil, stirring until the sugar dissolves. Spoon the beets snugly into jars, then pour the pickling liquid on top. Add a chilli to each jar, seal, and leave for a few days to infuse.