Welcome to this user forum.
BT do not deal with wireless issues, as there are too many variables.
Do you get disconnections if you connect your computer directly to the home hub using an Ethernet cable?
Which BT Home hub do you have, is it a home hub 5 or home hub6?
Ethernet seems to work ok.
Wireless connection can give problems.
Please could you try the following
First of all try a factory reset of the home hub.
Then turn Smart Setup off.
Also try separating and renaming the SSIDs.