Grilling the Meat. If you've marinated the meat in the refrigerator, take it out while the grill is heating up. Remove it from the marinade and place the London broil on the hot grill. Cook the meat for approximately 8 to 10 minutes on each side until the internal temperature reaches 130 to 135 F for medium-rare. Although the U.S. Department of Agriculture recommends cooking beef to a minimum of 145 F, cooking London broil to higher temperatures typically yields tougher meat.