Im sure virgin Tivo can record 2 and watch one? although I an not sure I dumped virgin 6 months ago and bought a box of the net which givers me alll channels
Dump the scart and use HDMI
Your virgin box will have an HDMI output and the TV if brand new will have a few.
As Smuggles says Scart are so 1990s they were designed for VCR.