I had a similar problem with no coverage in a brick-built workshop at the bottom of my garden so I ran an Ethernet cable from the BT Hub 3 down to a wireless access point (WAP) in the workshop, using exterior grade (black sheathed) cat 5e cable.
But a quick solution would be to get a Cisco 1230 or 1240 series WAP and connect that to your BT hub's EThernet connection and site it in the house near a window overlooking the garden. These WAPs can provide a rock solid connection over extended distances of several hundred metres - the 1230 will do up to 11 Mbit/s while the 1240 series can provide up to 54 Mbit/s connectivity. You can get them quite cheaply on eBay but do make sure you don't get the LWAP (light-wieght AP) version as these are useless for home applications (they use a central configuration server and won't work in stand-alone mode as you can't configure them locally).
Andy