Steve you would have to have a smoker or a method where you can put smoke on the meat but don't cook it. My smoker has a cold smoke setting where I can smoke things like cheeses, fish and meat without actually cooking it..You then have the smoke flavor but you can cook (fish, meat) the way you would regularly cook it...
Injecting works great but isn't totally necessary imo, if you use a good marinade.
The problem with the London Broil is that you are going to want to eat it medium rare and it is going to get to medium rare in a very short time in the smoker. Kind of not worth it unless you can get a heavy smoke on it. That's why i mentioned the cold smoking method.
If it was me, and it's not, I would go with Bru's advice and marinate it, grill it and cut it thin, against the grain. Can't go wrong there.
London Broil and flank are two of my favorite things to grill...