Wipe corned beef with a damp cloth; tie into shape and put into a large stock-pot or heavy-bottomed saucepan. Add enough cold water to cover and bring to the boil. Drain and rinse beef. Repeat this operation.
Cover brisket with boiling water; add salt pork, bay leaves and peppercorns; cover and simmer over low heat for 3 to 4 hours, or until meat is tender, adding chicken after first hour.
Cool slightly; skim excess fat and add carrots, onions, potatoes and turnips. Cook for about 20 minutes, then add cabbage wedges; cook until cabbage and vegetables are crisp and tender.
Serve the beef on a platter garnished with vegetables and with cooked beetroot. Accompany with horse-radish sauce and pickles.