Firstly, do you have a Tivo or a V6? They're different boxes - if you're not sure, check here . I suspect you have a V6, but it may help to confirm.
I can't imagine, off-hand, that a single white vertical line is what I'd term pixellation - that, to me, is picture breakup which doesn't tally with your description.
Can you post a picture of this line, it may help isolate what the issue could be. In the meantime, and as a simple test, have you swapped the HDMI lead & port on your TV?
I'm a Very Insightful Person, I'm here to share knowledge, I don't work for Virgin Media. Learn more
Have I helped? Click Mark as Helpful Answer or use Kudos to say thanks