In reply to a post by johnlowe:

Shall I try a reset of the HH, contact BT again?

Yes, I would.

The answer to this is it could be the HH5, and swapping it out is the easy way to eliminate that. If it's still not working properly at least that possibility is eliminated and then it's time to try something else.

My suspicion is it's something else, but try the swap first.