I am reluctant to touch the bell wire at the moment
Given you don't have any extensions, you can't do anything with the bell wire anyway, as you basically don't have one!! In Ezzer's post above, the bell wire on connection number 3 refers to if you have any extension sockets wired into the faceplate.
As regards whether you should try a SSFP (filtered faceplate), if there isn't any difference when using the test socket, and there isn't any difference whether you have a phone plugged into the filter or not, then given you haven't got any phone extensions, a filtered faceplate would be a waste of money for you, IMO.
Removing the bell wire only applies when you have extensions wired in, where the bell wire can act as an antenna, picking up all sorts of electrical noise which interferes with your ADSL.
Behind the master socket itself is BT's property - don't touch any wiring behind the master socket. That is why there is a removable faceplate - to allow people to install "hard-wired" extensions themselves without messing with BT-owned wiring.
Not sure what your broadband problem is, but if you've tried different routers, connecting leads etc, then with your phone setup consisting of a single master socket, it's unlikely to be anything at your end. Without knowing more details I can't comment further of course.
Hope that helps