No - you only need a license if you are watching something at the same time as it is being broadcast on live television, so past programmes that you are watching after they have been broadcasts do not require a license to view.
"You must be covered by a valid TV Licence if you watch or record television programmes as they're being shown on TV. It makes no difference what equipment you use - whether it’s a laptop, PC, mobile phone, digital box, DVD recorder or a TV set - you still need a licence.
"You do not need a TV Licence to view video clips on the internet, as long as what you are viewing is not being shown on TV at the same time as you are viewing it.
"If you use a digital box with a hi-fi system, or another device that can only be used to produce sounds and can't display TV programmes, and you don't install or use any other TV receiving equipment, you don't need a TV Licence. "
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