Given the OP has mentioned lack of training, can I highly recommend that you really DO NOT take a CAT with you. The moment you put a tourniquet on a limb you are basically saying that this limb is lost. Are you qualified to make that call?
You're better off carrying proper dressings, I have a SP Services T4 dressing that lives in my handbag. Most small first aid kits are little more than a pack of plasters and are useless in the scenario the OP is considering.
Water and torch have been suggested by most people (I use a Petzl E+lite). I also find a small compass really useful, not so much in an emergency, but when coming out of a tube station and needing to work out which way I'm going with no way to see the sun... oh, and carry more water.
Assuming you've survived any event happening on the tube, and you've made it to the surface, you're likely to find that the mobile network is down. I have a Delorme Inreach Explorer satellite communicator. Even if the cell network is down, I can still get a message out (even if just to twitter) so that people know I'm alive. I bought it for use when hiking, but it's now become a permanent fixture on my backpack.
Oh, and yes, you are being preppy