From the TV Licensing Technology page (my emphasis).

If you watch or record television programmes as they're being shown on TV you must, by law, be covered by a TV Licence, no matter what device you're using.

Many TV channels are now available to watch over the internet. If you’re watching programmes on a computer or laptop as they're being shown on TV, then you need a TV Licence. However, you don’t need to be covered by a licence if you’re only using ‘on-demand’ services to watch programmes after they have been shown on TV. So, you need a licence to watch any channel live online, but you wouldn’t need one to use BBC iPlayer to catch up on an episode of a programme you missed, for example.

Assuming I've interpreted this correctly; if you are watching only on-demand services, it appears a TV licence isn't required. It certainly wouldn't be required for your Lovefilm subscription, and apparently it wouldn't be required if you only use iPlayer for on-demand, rather than live streaming. I find this surprising personally.