Should I remove the ring wire, and why ?

The problem with a ring wire in a typical installation is that it creates an imbalance on the line. The telephone signal is delivered on 2 wires that are twisted together and are balanced. That is to say interference is reduced by essentially comparing the two signals and making sure they mirror each other. When the line reaches your house at the master socket there is a capacitor to generate the ring signal that is distributed on a single wire. This disturbs the balance of the line and also means that the ring wire acts as a nice aerial for picking up all sorts of radio signals and electrical noise.

So you could disconnect the ring wire and stop this imbalance, but your phones wouldn't ring right ? Well yes that would normally be the case. But you are doing this because you have ADSL on the line in attempt to improve it. So this means you must have a microfilter on every phone. The great thing is that each filter made to the UK spec has its own ring capacitor in it to make the phone ring and the ring wire from the socket is completely unused. Someone (maybe at BT) had the forethought to think that one through ! So you can safely run with the ring wire disconnected and microfilters on your phones. The only trouble being that if you move out and the next person does not have ADSL they will not have filters and then may find that some of their phones don't ring.

So the more elegant solution is to fit a filtered faceplate on the master socket. The filtered faceplate will remove the ADSL signal from your voice extensions and will generate a filtered ring signal that will not cause an imbalance on your ADSL. So when you have a filtered faceplate you leave the ring wire connected to the voice extensions so that they will all ring. This means also that they will still ring even if you get rid of ADSL.