At first I thought your problem was due to the V6 scaling bug, but if all other SD channels look okay, then I'm not sure what it is. Definitely have a read of that thread though if you haven't already so you understand the problems with the V6 video output. I have Sky Sports SD and it looks good on my V6, but I must admit it looks better on my older V+ which arguably has superior scaling abilities.
All I can suggest is play around with the video settings, as your TV is 4K I'd untick all the options apart from 4K & 4K passthrough. Also make sure aspect correction is set to "Panel". Also, as an experiment you could try unticking all the options except 576i and see if there is an improvement, as this way the V6 will output SD for your TV to do the upscaling which will definitely do a much better job than the V6. Of course you can't leave it like this but it would at least help in troubleshooting the problem.