BBC will be able to recover their costs from him
In an academic sense, yes, but more likely is that he stalls and appeals and leverages every excuse his job offers him and every weasel word in the Rules of Civil Procedure, and then drops the suit at the last possible moment before there's an order, and then appeals any claim for attorney's fees because it was dropped due to some fig-leaf explanation and not because it was without merit.
Eventually the BBC walks away vindicated in the eyes of anyone paying attention, and maybe with some settlement of their own, but almost certainly not made whole and their speech is at least somewhat chilled because they have to be good custodians of their budget, just as was always intended.
Maybe I'm jaded, but litigation with a ratfuck is ratfuck business. It can be a worthwhile investment if you have something other than money at stake, but it's inherently wasteful and awful.