You can't do thus because the V6 is an entirely different installation time than a TiVo. Hence you need to call in. At least at the moment. The engineer require longer to fit and check the box so that availability appointment you saw may not be long enough.
Sorry to hear that you weren't able to get an earlier appointment. I've checked this for you to see if I could reschedule the 13th for you and the reason you aren't able to reschedule to an earlier date online is because even though it shows an available appointment, there aren't enough hours left on that day to complete your V6 installation. Each installation job has a required amount of time to complete the work and even though there are hours available on the 13th, there's not enough time available for the engineer to install your V6 box.
As both @Parrotperson and @pgcowie advised, this is why you can't change the appointment time. This also means that anyone calling in for a V6 installation won't be able to have that date, so there's no queue jumping going on.
Virgin Media Forum Team
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Virgin media just turned an extremely disgruntled customer to a rather happy one. They called me this morning and changed my installation date from 3/02/17 to this Sunday, 11/12/16. Could not be happier, I honestly never thought they would call.
So it turns out that Virgin Media royally messed up and now have turned me back into a disgruntled customer. So yesterday was the day of installation, I woke up rather happy knowing I could finally enjoy some good tv later on in the day. My time slot for the engineer was 1-6. I happily waited around until 5:30, which is when I began to get suspicious that he may not turn up. I called up Virgin and they managed to get hold of the engineer who said he will still be carrying out the work, but his phone had died, so he will charge it and then phone me. At around 6:15 (past my appointment slot) he called me to say he is running a little late and would be with me in an hour. I thought to myself no biggie, i've waited this long. At 8:30 the engineer finally turns up with the v6 box in hand. I ask him exactly what work he was carrying out, as it was extremely dark outside so I couldn't imagine him drilling any holes to install the old tivo into another room. Turns out whoever booked the engineer didn't mention installing a cable into another room, he was only booked in to replace my old tivo with a V6. I phoned up Virgin and explained to them what is happening (whilst the engineer is still in my house). She tries to explain the engineer that we should be getting another cable installed in another room. The engineer refuses to do so as he says he would not be getting paid for that job as it is not on his system and because it is very late on a Sunday. So without wanting to cause an almighty fuss and with the possibility of waiting past Feb to get the install done I decided to take the V6 and ask them to come back to install the multiroom.
So this is an absolute joke because the main reason I upgraded my package was so that I could get multiroom for my wife while she recovers from surgery. This also meant a new (more expensive) contract will be starting from yesterday, which is an absolute joke, as i'm paying for a service i'm not fully receiving.
Whilst the engineer was installing my V6 he spoke to his manager who assured him someone would come out to install my multiroom today. No one has called me, so I decided to phone up Virgin. The best the virgin customer service could do was to EMAIL the area manager in hope that he will call me later and arrange an install for the second box.
So I still have 14 days to cancel thanks to a cooling off period. If they cannot send out an engineer to me this week, I'm afraid its the final straw and virgin will have lost a Loyal customer. It has been an absolute joke