One thing that could be causing issues is whether or not the walls are insulated. Insulated walls are a real pita for WiFi signal. The only way to get around it is more repeaters to boost the signal strength.
First thing you need to be aware of is that a wifi repeater made by X is unlikely to be able to boost the signal of wifi access point made by Y. You are going to have to pick a manufacturer and stick with it. When I was providing wireless internet access for student residences while at Uni we chose D-Link but with hind-sight Netgear would have probably saved us hassle as we deployed a Netgear solution to one of the houses we serviced and never got a call out because of broken hardware.
To start with you will need a Wireless Access Point. This will be the main device which allocates IP addresses and maintains security. After that you will need some Repeaters, some Access Points are multi-purpose and can also be a Repeater.
You will need to turn on the Wireless Access Point then walk throughout the house/building looking for potential weak signal points. If you can also check inside rooms do so. We had one person who at their door had great signal, but as soon as the door was closed and you moved a foot within the room the signal became unusable.
Once you have a picture of where the weak spots are you need to decide roughly where you can place other access points to boost the signal. The Repeaters/Boosters work best in areas of medium strength as they can get a good signal to themselves and boost for the best distance.
Something else to note if you wont always be able to access rooms is to try to place devices in stairwells and landings as you should be able to get to these at any time. The downside is that if anyone wants to steal any of your hardware they can get to them at any time. This relates to deploying wireless in a building you don't control, ie not your own house
Unfortunately I don't know of any suitable devices which will repeat BT HomeHub signal. A possible way around this would be to get a Wifi Access point from another manufacturer, then link this to the HomeHub via an ethernet cable. In this case the HomeHub would likely handle the allocation of IP addresses and the Access Point would only handle the wireless security.
An alternative would be to see if you can find a longer antenna for the HomeHub or get a separate wireless access point with a longer antenna. One of these options may be better than the other. Setting up Wifi is still a bit of a trial and error process these days unless you have very simple requirements.
