It's possible your iPhone is switching from your Home BTHub3/4/or5**** to BTWifi-with-Fon or BTWifi-X. These 2 slower networks are for other BT users and that's why BT say they have Millions of free Wi-fi spots!
On your phone's Settings/then Wifi check if your BTHub**** is showing; or is it one of the free wifis. If it's the latter then click on it and click Forget This Network.
Go back to Settings click on Wifi to choose your BTHomeHub****
I can't think of another reason your wifi is slow but there has been an update to iOS9, iOS9.0.1, which might help you.