The royal family's smoking history is hardly some big secret. It is very well known that King George VI smoked, that Princess Margaret smoked, that the Queen Mother occasionally smoked. You have to remember how extremely common smoking was back then. In the 30's and 40's and 50's, it was actually a little unusual NOT to smoke, so it's not at all surprising that Elizabeth and Philip once did so.
Queen Mary died at 86. She may have died of lung cancer, but she lived a long life.
Charles, however, is very concerned with healthy living and was distressed by the fact that his wife smoked. (She's said to have managed to quit finally.) Harry has sometimes been seen with a cigarette, but William has not, to my knowledge. I know of no members of the immediate royal family who are now regular smokers.
There may be members of the extended family who smoke, but if so, they've managed to keep it under wraps. It's obviously not acceptable today as it once was.
Edit: Amber, the Queen did smoke, and since her father himself wasn't even told that he had lung cancer, it's not likely that his wife and two daughters knew until after his death. Before then, both of the daughters smoked, and Margaret, at least, continued to do so. Bear in mind that the King died in 1952, well before any possible connection between smoking and lung cancer got any real publicity.