You can use the Chat function in the App. They do respond quite quickly (within a couple of minutes in my experience). From the main App menu select "Chat with us".
I've just been chatting with them again. 9 days ago they promised to correct the issue I had with a refund not showing in the balance. They told me this would be updated with 72 hours. But still no joy. So starting that process again. I've got zero confidence in this card and the company running it. It really doesn't reflect well on the BA brand (or the team at Head for Points who ran a promotion for this cr@p).
I've accessed the "Chat with us" functionality through the FAQ section. However, it doesnt seem to accept any text entry when I key in letters from my Android phone. Very frustrating!
I may just ask my bank to reverse the charge and let BA Mastercard sort it out