if you look at mathepacs drawing there is a cable in and out of every socket and finally it returns back to the board again, forming a ring basically.
A radial circuit doesnt have the final cable back to the board, which means there's an end of line socket, which only has one cable in it. If there is only one end of line socket in the sitting room, you can then run a cable from that socket to your new socket which would make your new socket the end of line socket!
The problem though, is you said there's more than one end of line socket in the sitting room. Are you sure about this?