Had a problem with my broadband dropping various times of the day usually between 6pm and midnight for the last 18months. I've had numerous engineers out who between them have replaced everything from my router bk to the exchange swapped lines over for me but it's still happening. I've had an rf engineer who came out to see if there was any internal interference there was not. I'm losing the will to live tbh. Bt admit there a network fault but seem to be doing absolutely nothing! When it works it's 50mb down 14 up. Just stability is a nightmare.
Do the lights on the BT Home Hub change colour when you get the disconnects?
Also, is there noise on your phone line at the same time?