Found an online PDF copy of your TV manual, and trawled a few spec-sheets, I've a nasty feeling you're snookered.
By means of explanation - it's a recent requirement, when watching OnDemand in 2160p (4K UHD) from a V6, that all your connected-equipment is compliant with HDCP2.2 (High-Definition Copy Protection) - there's some background reading here & Virgin's website has some further advice here
If some of your equipment is not compliant with HDCP2.2, then the chain is broken and this blank-screen behaviour is one of the symptoms (along with Error 603 or 604). There is no HDCP requirement when watching in 1080, and your TV will upscale to 2160 instead.
Most current 4K TVs support HDCP2.2 on all HDMI ports, some older ones only support it in one port. I can't see any reference to HDCP anywhere in the Toshiba manual, or any spec sheet - which strongly indicates the TV doesn't support HDCP2.2
If that is the case, you will be unable to watch OnDemand programmes in 4K UHD/2160 using this TV. Linear broadcast channels should be ok (for now).
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