I'm afraid my 'expertise' in these matters is limited to using google to find something which appears to be of relevance. But, sticking my neck out, I'd say not.
If you scroll down on Z-M's link you'll see that the person who started that thread did get the extender to work. (He probably just needed to read the instructions first!).
ANY make of wifi extender should work with your Virgin router, including a BT one.
I've got a Netgear extender - works perfectly well with my Virgin router - easy enough to set up too as long as the extender has a WPS button (most do).
They plug into mains sockets and use the house wiring to distribute your router signal - you plug one in by the router & connect with an ethernet cable, you plug the other one in where you need the signal - it will then broadcast wifi in the room concerned. Work very well usually.