I assume you have a "smart" freesat box with a network port or WiFi, that you want to connect to the Internet via your home router (presumably supplied by BT).
Its likely you can do that, if there are free Ethernet (network) sockets on the back of the BT router.
Suggestion:
1) Find the manuals
2) Read them
3) Google terms you don't understand
X, May 2015