For the crumpets, stir together the flour and salt in a large mixing bowl, and whisk in the yeast, the buttermilk and water.
Cover the bowl tightly with cling film and leave to prove in a warm place for one hour or until at least doubled in volume. Preheat the oven to 170C/325F/Gas 3.
Heat a frying pan until medium hot then add a little of the oil. Lightly oil the inside of four 8cm/3¼in metal rings then place them in the pan.
Pour or ladle batter into each ring to fill about half way. Cook the crumpets until the top has completely set, then remove the metal rings, flip the crumpets over and cook for one more minute.
Transfer the crumpets to a baking tray and bake in the oven for 10 minutes.
Serve immediately or cool on a wire rack until ready to grill.
For the hollandaise, place the butter in a saucepan and bring to a very gentle simmer.
Place the lemon juice and vinegar into a separate small pan and heat until just boiling.
Place the egg yolks into a food processor with a pinch of salt and switch on. With the motor running, add the hot lemon and vinegar then very slowly add the melted butter until it is all incorporated. Transfer the sauce to a small bowl, season with a little salt and freshly ground black pepper and keep warm.
Meanwhile, heat a frying pan until hot, add the bacon and cook on either side for 2-3 minutes until cooked through and crisp. Drain on kitchen paper, then roughly chop and add to the hollandaise. Stir in the chives to combine, then check the seasoning once more.
For the poached eggs, bring a pan of salted water to the boil and add the vinegar. Whisk the water to create a whirlpool and once settled, carefully crack an egg into the water. Simmer for 2-3 minutes then remove the poached egg carefully with a slotted spoon and place on a plate to drain. Repeat the process with the remaining eggs.
Heat a frying pan until hot, add the olive oil and cook the black pudding until crisp on each side. Remove with a slotted spoon and set aside to drain on kitchen paper.
To serve, place the crumpets onto serving plates and top with a poached egg. Pile the black pudding alongside then finish with a drizzle of hollandaise.