No, it won’t since rear window wipers are not part of the MOT tests. But it can make it harder to back up on a rainy day. If you’re thinking about removing it completely, you’re free to do so as long as there are mo protruding parts that can cause injury to any person coming into contact with it.
But the best option would be to have it repaired. My dad used to drive an old clunker that had a rear wiper that I’ve never seen work. One day he took it to a local garage here in Dartford to have the wiper replaced and it made such a huge difference. They did such good work that he could see through the rear window clearly enough to not hit our back wall every time he parked his car. If you’re considering going the same route, you can check out the garage he took the car to at www.claremontmotors.co.uk. I’m pretty sure that they can help you out.