It's possible that the format could be requiring slightly more processing/buffering within the box than is expected, especially if the BBC are pushing the content in a format not natively supported by the V6.
It's a demo rather than a release, but something it may be worth looking into whether it's possible to feed back to the BBC.
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I had the same too. Interestingly its the same when I stream 4k from my Amazon tv box. However I get no issues when I stream 4k from my NAS locally. I use my own modem rather than the Superhub, so imo it's the internat connection somehow.