Rub the beef all over with the olive oil and place in a shallow non-metallic dish with the garlic, cracked peppercorns and thyme. Rub all over the meat and cover with plastic wrap. Marinate for at least an hour at room temperature or overnight is best in the fridge.
To make the lemon aioli, break the egg into the blender and add the garlic, half a teaspoon of salt and the vinegar, sugar, lemon rind, mustard and half of the olive oil. Secure the lid and whizz for 10 seconds.
Leave to stand for a couple of seconds, then turn on again and pour the remaining olive oil and sunflower oil through the feeder tube in a thin steady stream. This should take 25-30 seconds.
Switch off the blender, take off the lid, scrape down the sides, and whizz again for 2-3 seconds, then season to taste. Transfer to a bowl, then cover and chill until needed.
When ready to cook, if using a charcoal barbecue, light it 30 minutes before you want to start cooking. If using a gas barbecue, light it 10 minutes beforehand.
Alternatively, use a griddle or frying pan.
Brush the excess marinate off the beef and cook over hot coals for 5 minutes, turning frequently until the outside is well browned, then transfer to a platter and leave to rest for up to 30 minutes.
Slice the beef as thinly as possible and arrange on a serving platter.
Invite guests to smear a slice of beef with a little of the creamed horseradish.
Add small piles of the beetroot, radish and watercress, then roll up and dip into individual bowls of the lemon aioli.