Put the potatoes in a large pan and cover with cold salted water. Bring to the boil, then reduce the heat to a simmer and cook for 5 mins until just tender. Drain.

Put the oil in a large roasting tin, then transfer the tin to the oven with the turkey for 10 mins. Remove the tin from the oven and carefully tip in the potatoes and thyme, turning to coat in the hot oil. When the turkey is cooked through, turn the oven up to 200C/180C fan/gas 6 and roast the potatoes for 40 mins. Turn the potatoes over and roast for 10-15 mins more until golden all over. Sprinkle over the chestnuts and roast for a final 10 mins until the chestnuts are heated through.