As this forum is for BT Retail customers, who have their phone service or broadband from BT, you would be better asking on the Virgin Media forums, as I think that they use a different form of caller display signal, which may be incompatible with your phones.
I have now confirmed that this is a design fault on the BT 6500 base unit.
I have tested two samples of the BT 6500 base unit, and both exhibit intermittent detection of Caller Display (Calling Line Identification) information. But the more modern BT 8600 base unit works fine in this respect. The BT 8600 also has a better answer phone.
It's a shame. The BT 6500 was so close to being an excellent product. Its dodgy Caller Display detector let it down.
Those having some old BT 6500 handsets kicking around, but who have upgraded to a BT 8600 base unit may be interested in the discussion at: