Good luck getting it fixed 
Yeah, lets look at the evidence:
* Using HH3 - known to be a pretty poor and non configurable box
* Pinging PC - no info if this is over WiFi or Ethernet and how loaded this PC is
No knowledge on how ICMP is redirected from the public IP on the HH3 through the NAT to a private IP since the forwarding on the HH3 is complex and non intuitive.
The packet loss could easily be between the VDSL modem and the users PC, and nothing to do with the BT service.
Only reliable solution would be to replace the HH3 with a configurable router and ping its public IP.
James BT Infinity 2 19/09/2012 - Estimate 44.6/6.5 - Install 52/12 - Actual 46 / 8 Mbps
Huawei VDSL -> Draytek router -> Apple Airport Extreme -> Belkin Switch -> Windows/Mac/Linux/NAS/Phone
13 years of broadband - 1999 ntl:(512k/1M)/BTbusiness(2M)/Metronet(2M)/Bulldog(8M/16M)/BE(19M/16M)/BT FTTC(46M)