The BT HomeHub 3 (HH3) was performing reasonably for BT Retail customers until the launch of Infinity 2, but since then it seems a bug has arisen either due to the extra load of handling faster throughput or a firmware upgrade. This bug manifests itself with Ethernet based connections only providing a speed of around 1 Mbps, where as the devices using wireless are able to still go as fast as the wireless network and underlying FTTC/P connection will allow them.
An important point to make, is that this bug only appears to affect people on the Infinity products, customers using the HH3 on an ADSL2+ service are unaffected. A solution was said to be in test back on 22nd June 2012, but posters on our own forums are still seeing the problem. In this specific post there is some suggestion that the TR-069 process that allows a broadband provider to remotely update/interrogate their hardware could possibly be part of the problem.
The general advice for people when experiencing the problem is either to connect via wireless or reboot the Home Hub. Hopefully a firmware upgrade will surface quickly from BT Retail, people are very much watching and waiting for it.