Hi Basilsauce,
Congratulations on getting the job - just to confirm that you will need 2 pairs of shoes. 1 set is for when on the commuting/walking through airport/boarding etc and the other set is for on board. That's why there are the two different requrements listed in the book. BA don't provide the shoes although sometimes they do have sales and things on in the crew report centre. Others on here may be able to give you more advice on where to buy shoes but you will not go straight into uniform during training anyway so you will have time to ask your trainers questions and get advice from them too.
Hope this helps