Lay the tomato slices in a grill pan. Mix together the basil and oil in a bowl, then drizzle over the tomatoes. Season with lots of salt and pepper. Cook under a preheated medium grill for 3–4 minutes until starting to soften. Arrange the bacon rashers on top of the tomatoes and grill for 6–8 minutes, turning once.
Poach the eggs, by breaking 1 of the eggs into a ramekin or cup, making sure not to break the yolk. Bring a large saucepan of water to the boil. Add the vinegar to the boiling water, then stir the water rapidly in a circular motion to make a whirlpool. Carefully slide the egg into the centre of the pan while the water is still swirling, holding the ramekin or cup as close to the water as you can. Repeat with the other eggs and cook for 3 minutes. Lift the poached eggs out with a slotted spoon.
Put a hot buttered muffin or slice of toasted bread on a warm plate. Top half of the muffin or the toast with grilled tomatoes and 2 rashers of bacon, then put the poached egg on top. Cook and serve the other 3 eggs in the same way, swirling the boiling water into a whirlpool each time before sliding in the egg. (Poaching the eggs separately ensures each serving is as fresh and hot as possible at the table.) Serve.