Thanks for responding, Danny.
I have tried both of the options you listed with no success, unfortunately.
I do not want to try changing my password (one of the suggestions I was provided) since I have several other streaming channels linked to that password and I fear such a change would mess up even more logins.
I'm going to give it another day or two to see if it spontaneously resolves itself or BritBox does, in fact, get back to me.
Failing that, I'll just cancel the subscription and maybe try resubscribing at some later date.