Firstly what do you mean by having 1 broadband? Do you mean you're a broadband & TV user, with your TV service being a sole TiVo? Or do you have 2 TV boxes?
The caveat - I would do some research into the pros & cons of 360 first, depending how many of the TiVo's recording features you use, I would just be very careful about migrating - just to avoid possible disappointment afterwards. Decide whichever, but do so informed.
Second - if you want the change, the best method is probably to get the TiVo swapped for a V6 first - the TiVo can't take 360 software, and the V6 is the same hardware as 360, just different software. Any box-move will need a non-fault tech visit which is currently backlogged due to being on-hold for several months.
You should then be able to just order an OTA software download to migrate the box software.
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Thank you so much for your post and I am so sorry for any confusion surrounding your upgrade.
Of course this is possible for you and you can call us on 0345 454 1111 or 150 from a Virgin landline to discuss with a sales agent. If you have any questions around the service at all I'd be more than happy to help. Just let me know!