This sounds like a signal issue, manifesting as picture breakup. I'd expect you to get signal related error codes too - possibly (but not guaranteed) W02.
You'll probably find the random channels all share a common broadcast frequency without your realising. I'd also expect- so I'll ask - OnDemand should be unaffected, it uses the internet unlike live TV.
If you've rebooted the boxes, then there's an underlying fault. Check for existing issues first by calling 0800 5610061.
If nothing's listed, then it's probably only affecting you and you'll need to report it. Either by calling VM or by waiting on here.
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