I have recently started having issues with opening the HomeHub 3.0 device web page - usually this issue can be resolved be switching the device on/off 1-2 times, but I'd prefer a more convenient resolution.
When this problem occurs the HomeHub device is no longer visible within Network Computers and Devices - however, internet access remains completely un-affected (I'd like to emphasise these points because they went completely over the heads of BT Support - i.e. the device is working, but isn't accessible).
BT Support suggested that something was blocking the device web page, however this seems inconsistant with the device not being visible on the network - and that it becomes visible after it is re-started.
I'd be grateful if anyone could anyone explaing the problem and potential solutions.
Can't help beyond saying that when I had a HH3b it did exactly the same thing from time to time. It still functioned perfectly well as a router and, as you say, internet access was unaffected - it was just impossible to access the hub's web interface.
I subsequently moved to a HH4 and, shortly after, a HH5. Neither has ever had the same problem. So, for me, it was just something a bit tiresome that the HH3 did.