No you don’t. As you’re not watching or recording live TV, you don’t need a licence.
Live TV means any programme you watch or record at the same time as it’s being shown on TV or live on an online TV service. See what counts as ‘Live TV’.
Services that provide on demand or catch-up include: BBC iPlayer, ITV Hub, All 4, Sky Go, Virgin Media, BT Vision, Apple TV, Now TV, YouTube, Roku and Amazon Instant Video.
Remember, if you watch or record live TV on any device, you need to be covered by a TV Licence.