To make the Hollandaise sauce – in a bowl place the lemon juice and the white wine vinegar, add the egg yolks and whisk together until the mixture is light and frothy.
Place the bowl over a pan of simmering water and continue whisking until the mixture thickens. Add the melted butter slowly, whilst still whisking until all blended and thick. Add the salt and pepper and set to one side, covered to keep warm.
In a pre-heated grill, cook the bacon until crispy and then keep warm. Place your eggs into poach your eggs for three minutes; in the mean time place your halved muffins into toast, remove and butter. After 3 minutes remove your poached egg with a slotted spoon.
Put two bacon rashers on each half of muffin, place one egg on top of this and pour the Hollandaise sauce over, season and serve.