This is what the Licence people state:-
You need a TV Licence if you:
- watch or record live TV on any channel or service
- use BBC iPlayer
You may be able to get a free or discounted TV Licence if you’re 75 or over and get Pension Credit, or if you’re blind or in residential care.
You do not need a TV Licence to watch:
- streaming services like Netflix and Disney Plus
- on-demand TV through services like All 4 and Amazon Prime Video
- videos on websites like YouTube
- videos or DVDs
So being pedantic BBC programs that are repeats or pre-recorded would appear to be license free over the air.
I've always question what constitutes live - because by the time it gets to me its probably a few milleseconds later