Try to find true bangers (British pork sausage) for this comfort-food classic. Deglazing the pan with red wine makes the onion gravy extra flavorful.
Put potatoes in a medium pot and cover with cold water. Add 2 teaspoons salt. Bring to a boil. Reduce heat to medium-low and simmer until tender, about 10 minutes. Drain potatoes in a colander and return to pot. Mash potatoes with butter, milk, cheese, and a few gratings of nutmeg. Season with salt and pepper. Keep warm.
Meanwhile, preheat a large skillet over medium-high. Add oil and bangers. Cook, turning occasionally to brown all over, about 6 minutes. Remove bangers to plate. Return skillet to medium heat. Add onions and cook, stirring occasionally, until softened and browned, about 8 minutes. Add wine and cook, scraping bottom of pan with wooden spoon to release brown bits, until reduced by three-quarters, 3 minutes. Add flour and cook, stirring, 1 minute. Stir in broth, soy sauce, and Worcestershire. Return bangers and any accumulated juices to skillet. Bring to a boil and cook, turning sausages several times, until juices thicken to a gravy-like consistency and bangers are cooked through, about 8 minutes. Serve with mashed potatoes.