They were with BT.
Given that you said that in your original post that they had BT broadband I can not see why this is becoming such a drama. It would appear to be a database fault so I am at a loss to see how this can not be easily resolved for you.
Perhaps you should look at another provide who may be able to do something about resolving this!
Until the OP is a customer it's unlikely BT would do the running around to get the database sorted, with the risk of the customer then going to a competitor.
Well the ain't going to get him as a customer if they can not guarantee that they can supply the product he wants without him taking a risk that they will be supply it once he has signed up.
Webby - you've probably got to the heart of the issue there. But Openreach are unwilling to resolve it either. The words rock and hard place spring to mind.
Alternatively, if they had any nous at all, they would pull out all the stops, sort out the problems and gain a customer that would spread the word that what a good company BT was!! Sorry, I was dreaming there.