You'll need to ditch the HH and buy a router that actually has some configurability to it - BT have taken the view that any feature not used or understood by a large number of customers is to be removed as it may increase support costs.
I bought an Asus wl-500w new from ebay for around £30, to get maximum features I put dd-wrt open firmware on it, but just to enable dns you don't need to go that far. I changed to setup OpenDNS on my router and to enable me to lock down my daughters PC to 2Mbps (nasty Daddy - but Skype was using all our download allowance).
Hopefully BT will see the light at some point and allow basic router configurability on the HH3.
You cant do it on the home hub, but their is nothing to stop you setting one or more DNS servers manually on your PC (or Mac)