Mince the garlic to a paste with salt and in a blender blend with the salt, red wine, balsamic vinegar, soy sauce and honey.
In a heavy-duty sealable plastic bag, combine London broil with marinade. Seal bag, pressing out excess air, and put in a shallow baking dish. Marinate steak, chilled, turning occasionally, at least 4 hours and up to 24.
Bring steak to room temperature before grilling. Remove steak from marinade, letting excess drip off, and grill on an oiled rack set 5 to 6 inches over glowing coals, 7 to 9 minutes on each side for medium-rare. Transfer steak to a cutting board and let stand 10 minutes.
Holding a knife at a 45-degree angle, cut steak across grain into thin slices and serve with tomatoes.