Heat the oil in a large pan over medium heat. Add the stewing beef and brown it on all sides. Do this in batches if necessary to avoid crowding the pan.
Add the kidneys to the pan and brown them as well. Cook for about 2-3 minutes, then transfer both the beef and kidneys to a plate.
In the same pan, add the chopped onions and garlic, cooking until soft and translucent (about 5 minutes).
Stir in the flour and cook for 1-2 minutes to get rid of the raw flour taste.
Gradually add the beef stock, stirring continuously to avoid lumps. Add Worcestershire sauce, tomato paste, salt, pepper, bay leaf, and thyme.
Return the beef and kidneys to the pan, reduce the heat, and let the mixture simmer for 1 hour, or until the meat is tender. Stir occasionally and add a little more water if necessary to keep the mixture moist.