Toss the potato wedges with 2 tablespoons of the oil, the thyme and a pinch each of salt and pepper. Tip onto a large baking sheet and bake in a preheated oven, 200˚C (400˚F), Gas Mark 6, for about 25 minutes, turning occasionally, until tender and golden.
While the potatoes are cooking, place the sausages on a small baking sheet or in a roasting tin or ovenproof dish. Drizzle over the remaining oil and cook in the oven for about 20 minutes, turning occasionally, until cooked and golden.
Meanwhile, mix together the honey and mustard. After 20 minutes, remove the sausages from the oven and pour over the honey-mustard mixture. Turn to coat, then return to the oven for 4–5 minutes until sticky.
Remove the sausages from the oven and cool slightly before serving with the potato wedges and plenty of green salad and/or coleslaw, if desired.