I think you got it right with the 'guess' part at the end Andrew, having pulled the 300 day figure out of the air and tried to pass it off as fact I think you saw a router doing DHCP at work once and assumed that's how Virgin did it.
Read your DHCP lease, they are 7 days, they expire after 7 days, if you're looking at the DHCP leases on your PCs they will of course be different as they are getting leases from your IPCOP box. That lease length will vary depending on what's in your dhcpd's config.
That you seemed to think dial up IP address allocation ran in a similar way to cable and other DHCP based services says you have no idea what you're talking about.
I seriously doubt you knew that Virgin use Cisco Network Registrar, and as CNR is a DHCP standards compliant server it has no relevance at all to DHCP leases anyway, these being set as per normal. The only extra parameters are Cisco specific AV-Pairs which are nothing to do with this discussion.
Think it's best if I stick you on ignore, I'll just get myself into trouble if we keep going down this route.