They fear pirates, so what about...
Printing/secure e-mailing an annual code with each paid-for TV licence and permitting that to be used to gain access to the service (like the "key" that has been mentioned here, but licencee specific)?
Sure, some folks might foolishly share their key, but couldn't the beeb throttle traffic destined to devices using the same key (with a rapid drop-off in per-channel through-put when, say, more than 5 devices are pulling data concurrently against the key)?
Allowing *any* client to then pull the data seems fine to me at that point because massive-scale sharing of any given key means that key becomes essentially unusable.
This makes it possible for the beeb to focus on the service and forget about trying to craft support for all those clients, as has been suggested in earlier comments, since communities will do it for them.