@Hitchhiker, thanks for that pearl of wisdom!
You are absolutely correct, my logic tells me that if something is "Embedded", then it has "become a part" of what ever is the subject matter "overlay" however suggests to my simple mind that it has just been laid on top of it!
My command of my own language often leaves me speechless!

I have just followed the tutorial you linked me to and waited with baited breath for the possibility of success, sadly, after 15minutes, this was the result:-

It could only happen to me!
Why on earth has VLC taken it upon it's self to rotate the video 90°?
The "Subs" are certainly there but attempting to play it on my TV, I'm told "Playback not available"!
I have since been experimenting with get_iplayer using the command "--subs-embed" and although they play and display the subtitles in VLC, they don't show up when played on my TV
As you point out, since they are embedded, they are "selectable", but the default is "Off" hence they are not shown when played on my TV.
The reason I'm attempting this is for my winter holiday in Mallorca. Our 2.1m dia. Sat dish has blown away!!!
The general consensus is that we should not replace it due to cost and the maintenance required to keep it "on track".
Don't know if you've been to Mallorca in the dead of winter, but the wind is reminiscent of my many visits to Amsterdam in November but there is not as much to do!
Another possible route might involve taking a FireStick, which I bought in December but have not yet unpacked!
I'm led to believe that it would allow me to view the content of my External drive, via VLC and as I understand it with "Kodi", of which I have equally little experience or knowledge!