Heat the oil in a frying pan. Add the onions and cook over a low heat for 18–20 minutes, stirring from time to time, until they start to caramelize and turn golden. Stir in the crushed garlic and cook for a further 2 minutes, then stir in the Worcestershire sauce and thyme leaves and remove from the heat. Leave to cool.
Transfer the onion mixture to a bowl and stir in the yogurt.
Juice the horseradish and add the juice to the onion dip. Season to taste and serve.