Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the butter and oil in a large frying pan, add the lamb, onion and leek and fry, stirring, until the lamb is lightly browned.
Stir in the root vegetables and barley, then add the stock, allspice, rosemary and plenty of salt and pepper and bring to the boil, stirring. Pour into the slow cooker pot, cover with the lid and cook on low for 8–10 hours or until the barley is tender.
Stir well, taste and adjust the seasoning, if needed, then ladle the soup into bowls. Garnish with chopped herbs, if liked, and serve with warm bread.