Preheat the grill to medium-high. Preheat the oven to 120°C, fan 100°C, gas ½.
Grill the sausages for 15 minutes, turning occasionally, until golden and cooked through. Add the tomatoes, cut-side up, and the mushrooms for the last 10 minutes of cooking. Remove from the grill and keep warm in the oven.
Heat a large frying pan and add 1 tablespoon oil. Add the bacon and fry until crisp and golden on both sides. Remove from the pan and keep warm.
Fry the bread in the pan for 2-3 minutes on each side, until golden. Add 1 tbsp oil to the pan, then fry the black pudding for 2-3 minutes, until crisp on both sides. Remove from the pan and keep warm.
Place the baked beans in a small saucepan and simmer for 5 minutes.
Meanwhile, heat the remaining 1 tablespoon oil in a clean, large frying pan, then crack in the eggs and fry until the white has just set and the yolks are still slightly runny.
To serve, divide among 4 plates and serve with mugs of tea.