I probably bought from them before "rush hours" (in early November) so your experience might differ, but I had no trouble contacting Black Arrow (to cancel a mistaken order and direct the funds which I had already dispatched to them towards another order with my name on it). I wasn't asked for any additional documents since I paid from my own account and ordered in my own name. The whole process took 4 days, but this included weekend.

(The need to cancel one order and use the funds towards another order resulted from my mistake. Unfortunately it demonstrates that even customers who generally do read the fine print occasionally make mistakes, and with running a shop comes the burden of having to support them. I realize it's difficult for a "mostly engineering" shop to support a lot of customers - especially customers who speak many different languages. I thus try to not bother them with excess curiosity.)