The elephant in the room: or, the what-no-one-ever-tells-you department.
If a broadcast signal from a BBC transmitter could be received in deep space, the signal would not necessarily be understood.
Let's imagine a little green man living at Alpha Centauri, the nearest star to us. If he detects a BBC signal, can he recognise it? In the 1960s, when pulsars were discovered astronomers detected them - and thought that they represented intelligent life - because they were, or were thought to be, obviously artificial.
A pulsar emits a very regular pulse of radio waves, i.e. it emits a very consistent number of pulses a second. The astronomers equated the fact that the pulses were regular, not random, with intelligence. It was only because the signal was regular that they found it, or paid any attention to it.
A tv broadcast is not a regular signal. It might superficially seem to be, because it runs at 25 frames a second, but the actual signal content is not the same from moment to moment. We use modulation of the signal to carry information, but that very modulation is what Pulars lack. So would a tv signal be recognised as indicating intelligence? We already know that a pulse emitted 25 times a second can be sent by a Pulsar, which is a completely natural phenomenon.
Further, could a little green man decode the signal? In fact, you need to know quite a lot about the assumptions made by Marconi/EMI in 1936, when they invented the 405-line VHF system, in order to decode it. The signal seems to be 25 frames a second, but is actually 50 fields a second, interlaced.
Supposing E.T. knows what a second is, if he wants to decode the signal he will have to receive it on a 50 Hz frequency, and then interlace it in pairs of adjacent fields. But does he know how many scanning lines per field are being used? If I know that it's a 405-line signal, I probably couldn't decode it properly, because in practice not all 405 lines were used for the picture!
To hear the sound, E.T. will have to detect also the audio sub-carrier frequency. For a BBC2 transmission, or a post-1969 transmission, he also has to detect a 3rd signal, which is the colour sub-carrier.
To understand the sound, he has to take a quick course in English at the University of Alpha Centauri. Perhaps that is the trickiest step of all?
What-they-never-tell-you, part 2:
Did they remember to tell you that the world spins?
Sadly, that means that the BBC also spins. A UK transmitter is only above the horizon, viewed from a fixed point in space, such as Alpha Centauri, for half the time. Although a Pulsar emits its signal continuously, a BBC transmitter can't, because the BBC invented a concept called 'closedown'. In the 1960s, it only transmitted during limited hours. And as the world turned, too, for half of the time the BBC was out of sight from Alpha Centauri.
Actually, it was always out of sight. You'll have noticed that when you look up into the sky at night, in England, you don't tend to see Alpha Centauri! It's a star that's only visible from the Southern Hemisphere. So E.T. was actually receiving repeats on the ABC in Oz, because he never can see Britain from Alpha Centauri. That's another snag of watching tv in space!
And finally, Cyril...
And finally Esther: You probably don't need to be told that A.Centuri is a star about 4 light years away. That's great for watching tv programmes which aired in 2017, not so great for watching Dr Who in 1964. For that, you'd need to be about 14 times further away.
The inverse square law is a bit of a snag at 4 light years: it drives signal strength way, way down. At 57 light years, you'd need a miracle to detect a signal against a background of random galactic static.
