We have put together a short survey to capture your feedback in terms of what BT can do when you experience home Wi-Fi issues. We would appreciate it if you could take a couple of minutes to complete a short survey. Read more from here, Fix my home Wi-Fi
Can you post your line stats from the HH5 please? These are in Troubleshooting/Helpdesk on the web interface at http://192.168.1.254
Lines 1-13 will be enough
Oh sorry, the lack of line stats could be a problem.
Instead can you run this speedtest please and post the graphs, or a link to the results? http://labs.thinkbroadband.com/ispa/