But it's perfectly legal to own a TV and use the on-demand portions of iPlayer (everything apart from viewing the currently-being-broadcast channel streams), Netflix, Google Play, 4od, Demand 5, DVDs, Blurays, etc etc.
This is what I do. The TV Licensing website has a page where you can provide them with your reasons for not owning a TV license. This page explains (implicitly) all the things you can do sans license. And, hopefully, filling this in makes them less likely to pester you (I haven't had any contact from the licensing people).
Here is the text from TV Licensing:
You need to be covered by a valid TV Licence if you watch or record TV as it's being broadcast. This includes the use of devices such as a computer, laptop, mobile phone or DVD/video recorder.
Note how the second sentence arguably introduces confusion. You don't need a license if you use a computer but don't "Watch or record TV as it's being broadcast".