Sorry to add to the doom and gloom, but if it all kicks off in Iraq then there won't be any recruitment at BA (or anywhere else!) for a long, long time. They are in the process of shedding a large number of flight crew positions through "Future size and shape" most of which will come about through retirements and a freeze on recruitment. You only have to look at what happened during/after the gulf war and combine that with the current dismal situation to realise what the result on recruitment would be.
You are right in that BA's cadet program is a good (and cost effective!) way into commercial aviation but as you say don't put all your eggs in one basket, when i applied back in 1990 they had 40,000 applications for the 100 places. You do the maths. I was hired in 1998 by a leading Charter airline, having been a self improver. There is life outside BA and in recent times the gap in pay and conditions has narrowed considerably, so consider all the options. Timing is absolutely critical, i think now might be a good time to start training. I started in 1994 when there was very, very lttle recruitment going on, but by the time I finnished training things had picked up and i was in the right place at the right time and got lucky! But the window of recruitment never stays open for long! If things stay as they are (!) then in 2/3 years should catch the next up swing in the industry.
Best of luck! Go with the flow and be prepared to roll with the punches!