To make marinade: In a bowl, whisk together marinade ingredients until combined well. Put London broil in a large resealable plastic bag and pour marinade over it. Seal bag, pressing out excess air, and set in a shallow dish. Marinate meat, chilled, turning bag once or twice, for 8 hours.
Remove meat from the marinade, discarded the marinade, and pat the meat dry.
Preheat a grill and on an oiled rack set about 4-inches over glowing coals, grill the meat, turning each once, 9 to 10 minutes on each side, or until it registers 125 to 130 degrees, on a meat thermometer for medium-rare meat. (Alternatively, meat may be broiled.)
Transfer meat to a cutting board and let stand 10 minutes. Cut meat diagonally across the grain into thin slices.