Radio licences were phased out when transistor radios the size of a mobile phone came in. They just couldn't keep track of them, so gave up trying to collect.
Your TV licence is to allow you to operate a 'television broadcast receiving apparatus'. If your TV is for video only, it doesn't count. BUT! When the TV police call at your door, you must be able to convince them that you don't watch live TV on it. They're a cynical lot, and not having an aerial connected simply won't do. What you really need to do is disable live TV reception. Get inside the TV back cover and cut the connection between the antenna socket and the tuner unit, (a small rectangular metal box that the cable runs to). If they call, you can show them the connection is cut, and they'll accept that as proof that things are as you say. It's a palaver, and I look forward to the day when TV licences are done away with.