Preheat the grill and cook the bacon until crisp, turning occasionally. Set aside on kitchen paper to cool, then roughly chop.
Whisk together the eggs with the milk and season. Heat the oil in a non-stick pan then add the eggs, and allow it to set for about 30 seconds, without stirring.
Start to slowly stir the eggs with a wooden spoon until they are softly set but still slightly runny.
Add the bacon, red pepper, spinach and cheese to the eggs. Stir until combined, the spinach has started to wilt and the cheese has melted.
Divide the mixture between the four wraps and roll up into burritos. Serve with wedges of lime on a serving tray.