I am afraid that you cannot use a keyboard with the v360 it will only pair up with the remote that is supplied. The USB socket on the back only supplies voltage there is no data signal so you cannot place a dongle in the back.
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There is no reason why the TV 360 and V6 boxes shouldn't support a keyboard be it wired (USB), wireless (USB dongle) or Bluetooth. I used a Telewest Infrared keyboard that I bought on eBay with my Pace and TiVo boxes. It was useful for searches, series links etc. as well as the cwctv.net e-mail service although I rarely used the latter, I just registered for fun.
Typing using the remote can be tedious and, while I accept that there is voice control on the remote, it doesn't suit everyone and it's not always accurate.
I find that saying "fast forward two minutes" is often interpreted as "fast forward to minutes" which changes the mode to slow fast forwarding. I usually say "advance a couple of minutes" but sometimes I forget because the rest of the time I'm using numbers "three minutes", "four minutes", "thirty seconds" etc.
While watch TV yesterday afternoon I came up with an even better reason for keyboard support on the TV 360 box.
Not all TVs are 'smart' TVs and not all 'smart' TVs are all that smart. There is significant opportunity for Virgin Media to bridge that gap by adding a web browser to the apps available on the TV 360 which would necessitate support for a keyboard.
many smart TV and fire TV have browsers. But stats from providers show that no one uses the TV for browsing. You would also have to support all the code needed like java script, HTML5 stc and that could become a security risk to the platform