Can you even claim copyright on something you no longer have a copy of yourself?
Doctor Who
A good old fashioned Doctor Who Community
Yes.
There is nothing in the law that makes that a relevant factor, and there are simple examples where you'd clearly not want it to be. If I was working on a novel, sent a copy to an editor, but then my hard drive crashed, it'd be more than a little annoying if that suddenly voided my copyright and my publisher then proceeded to publish my novel without giving me any money at all since it's suddenly become public domain.
I get the point you're trying to make, but this isn't the kind of thing you generally build into law because there are always edge cases that can cause problems. It's simpler to correctly assume that the copyright holder almost certainly won't object the existence of the copy while retaining the rights to them.
So unless I missed something, I didn’t see any place where the BBC went after the collectors for illegal recording. This sounds like they’re scared of something that hasn’t happened and, at least in this case the BBC is very happy to have found a copy.
The article states what they are worried about
This would reassure British amateur collectors that their private archives will not be confiscated if they come forward and that they will be safe from prosecution for having stored stolen BBC property, something several fear.