You guys are assuming that the specifics of DBA works the same in England.
There's no point in setting up a DBA with a limited liability entity. Why? You're basically saying, "I don't want the limited liability".
I don't know the specifics of this transaction, and it really, really looks sketchy. The only reason I even think it has credibility is because it was posted in detail on HN. In most other forums, I would chalk this up to a Nigerian scam. Seriously.
I still think there may be a way to pull out the money if the English Ltd has actually been established and the OP has control over it. Having the English Ltd establish a bank account, pull the money from that. If Apple balks over that, than that really is Apple's fault. As the situation stands though, if the OP went public over this, I think I'd have the same reaction as the lady who sued McDonald's over spilling her own coffee on her lap, or those patent trolls out in Texas.
It just means it's a name you are using, but it's not your name.
All non-corporation company names are legally fake names.