You can call the correct number on +44 208 707 4492.
As it is a 24hr number manned by extremely competent staff in the UK there may be a short delay if someone has to "wake-up"!

Or email as suggested above, but give them the exact flights you want.
BAH will also happily put you on another airline if there is something that will get you there in better order.

Edit: AA has a seat in F on AA81 to DFW today (2.05pm); onwards to LAS on AA1459.
Enjoy some FFD during the layover.
Or use AA135 to LAX and do an overnight there (you will have to pay for a hotel and claim back but I recently had a $550 dollar claim paid without question - I had a copy of an Expedia search for airport hotels).