Such problems are usually associated with rights issues. However I wonder if the programme you're seeking might not simply be 'hiding' somewhere on Virgin's BBC iPlayer app? (i.e. it's not been properly 'indexed' even though it's actually there)
That's because I've just looked for W1A on the BBC iPlayer app on my Now TV box and, like you, I've (initially) found that it's not there. (i.e. I've called up the list of programmes beginning with W and it's definitely NOT in the list). However going to the 'search by name' feature, and entering 'W1' immediately brings it up (as, indeed, does going to the 'Channels' list and looking at BBC Two).
So perhaps it's there all the time if you simply look a bit harder?