Sounds to me like you're describing picture breakup and/or pixellation that's usually the result of a signal fault.
If you've restarted your box once, then you're best calling Virgin Media on 150 (or 0345 4541111) to report your fault. Chances are you need either a replacement box or for an engineer to investigate further.
In the meantime, are there any specific channels affected? You've mentioned ITV/BBC, not which ones or if these are the HD/SD ones?
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