Mary, welcome to FT. Firstly let me say that fear of flying is very common (even amongst people who regularly do it!) and can stem from many sources, some rational, but most irrational. I'm not trying to pooh-pooh it, my father suffers from fear of flying also, but I have found that it is little use bombarding him with facts and figures, because at the end of the day his fear is largely irrational, although perfectly understandable. I myself suffer from vertigo and get a bit dizzy and break out in a cold sweat when up a high building (i.e. Sky Tower in Auckland) - totally irrational, but I can't help it!!!
Of course, both BA's 747's and 777's are very safe, in fact any aircraft that BA flies is safe, as it is one of the world's top airlines with an excellent safety record.
BA and Virgin both run good day courses which it may be worth attending - the usual format is a morning of presentations and meeting the crew and talking about flights, aeroplanes and fears. Then a flight in the afternoon where the crew talk the passengers through every stage of a flight and explain exactly what's happening at each stage. I've heard they are very good (I saw one on Airport once). Here is the link to the Virgin programme
http://www.virgin-atlantic.com/en/gb...ithoutfear.jsp
and BA
http://www.aviatours.co.uk/
Good luck with it - the ability to travel the world really does make it worth it in the end!