Preheat the oven to 170ºC/350ºF/Gas 3.
Rinse the kidneys and pat dry with kitchen paper. Cut the kidneys, in half, snip out the white cores and cut the kidneys into roughly 1.5cm pieces.
Place the cubes of steak into a large, strong plastic bag and the kidney pieces into another bag. Divide the flour between the two bags, then season, to taste, with salt and freshly ground black pepper. Tie the ends of the bags and shake until the steak and kidneys are thoroughly coated in the seasoned flour.
Heat two tablespoons of the oil in a large non-stick frying pan and fry the steak, in batches, over a medium heat, adding extra oil as needed, until the steak is well-browned all over. Remove the steak from the frying pan with a slotted spoon and transfer to a flameproof casserole.
Return the frying pan to the heat and repeat the process with the kidneys, frying on both sides until well-browned. Remove the kidneys from the frying pan with a slotted spoon and transfer to the casserole.
Return the frying pan to the heat, add the remaining oil, then add the onion. Cook the onion over a low heat, stirring often, for five minutes, or until softened. Stir the cooked onion into the casserole with the beef and kidneys.
Deglaze the frying pan with the wine, bringing it to the boil while stirring to lift all the browned bits from the bottom of the pan. Pour the mixture immediately over the beef, kidneys and onion.
Strip the thyme leaves from the stalks and add them to the casserole. Stir in the bay leaf, beef stock and tomato purée.
Bring the beef mixture to the boil. Remove three ladlefuls of the sauce for gravy and set aside in a small pan to cool. When cooled, set it aside in the fridge for use as gravy.
Cover the casserole and transfer to the oven to cook for 1½-2 hours, or until the beef is tender (stir the mixture halfway through cooking).