As stated, the call-blocking phone is your best option in this scenario. It does mean waiting for the phone to be delivered, and for that matter it also means shelling out for another phone that you probably don't need, but in the scheme of things it's still the optimum solution. Even if BT or any other provider could or would block all numbers whose CLI included the Birmingham code ( which I doubt ), by the time you got them to do it, you'd still be better off just getting the new phone and have done with it - although I'm bound to ask, if you do want to pursue the idea of asking BT to block that code, surely the easiest thing ( and yes, knowing how long it can take to reach a human being at BT, I do use that word in it's most generous sense ) would just be to call BT and ask them?
I think we know that you know that the calls aren't actually coming from Birmingham, but the point is that if this particular scammer actually does have that much of a grudge against you ( and they're usually thicker-skinned than that - they have to be! ), they could just spoof a different area code and carry on changing it indefinitely for each area code that you block ( again, if that were possible ). I'd love to know what you said in the first place that p*ssed them off to that degree - I'd try it myself!! - as I've never known a scammer, either as an individual or a company, to waste their own time in a pursuit like this.
In the short term, you might want to think about either unplugging the phone ( unless you have a dozen phones ) or leaving it off the hook. I know, before you say it, that that's inconvenient; but if the scammer is calling regularly and often enough that it's actually blocking your line as you say, you're not going to be any worse off, and at least the phone won't be ringing every five minutes.
P.S.: Just read the last couple of posts: I'm not familiar with the technology you're referring to, but if you can do that, once again, it'll be a sight quicker than investigating the possibility of BT doing it for you - which, as has been said, they almost certainly can't. Even then, though, the scammer can still spoof from a different area code once they twig what you're doing.
