Yes it is indeed possible and I recommend that you use "Home Plugs" to send the Internet signal to the Freeview box.
Here is an example from BT:
These boxes use your home's electrical wiring to send the Internet signal through your home. It is more reliable that using a Wireless connection.
You plug the transmitter into your router and into a power outlet. The receiver is then plugged into where the Freeview box is located and a computer cable connects your Freebox box to the receiver.
You only need to make sure that your router or Freeview box are not plugged into surge suppressors as these will affect the signal.
Another solution is to use a "range extender" which takes your exising Wifi signal and extends it. However I have found that Home Plugs give a better result.
If you have any further questions, please press "Reply to Expert" rather than rating my answer.
Would it be possible to use a USB plug in wireless adapter/dongle or would a Home Plug be better
I would recommend the Home Plug over a wireless solution especially as you have multiple floors to penetrate.
Here's a good article
Let me know how you go.