I think it depends on where you are. If you are in the UK (a guess by your name), it seems the BBC has an iPlayer available for the devices noted in your link and I would guess you can download from it (or the desktop version) to these devices to watch later. Check the UK Google Play Store.
If you are not in the UK, the Beeb produces an iPlayer for Canada and, I think, Australia and New Zealand - but not for Android. For the iPhone and iPad only. I've been onto them about this and, while sympathetic, no real plans stated. Pity. It's another reason I have yet to give up entirely on my iPhone (I'm in Canada), but a heck of a thing to watch programming on.
I note there's some sort of unofficial workaround app in the Canadian Google Store, but it all looks kinda dodgy and hasn't got great reviews - so if you're living outside of the UK and in one of the 'colonies' where the iOS BBC iPlayer is available and really want the service, you might be better served to look at a iPad Mini.