YouTube on a V6 uses the internet, so a good test to start with is whether other functions that also use the internet, work. Can you try watching an OnDemand programme and see if that works? Find a programme from ITV, C4 or C5 CatchUp and try watching it.
If that works, the V6's internet connection is working and it could be an issue specific to the YouTube app. In this case a restart is the next thing to try - via Home > Help & Settings > Clear or restart, and following the onscreen instructions.
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