From what you say is happening, it looks like the phone line goes into the alarm first and then out from there.
I think that the incoming line is marked Ring and Tip, and the outgoing cable is marked R and T. So in theory, if you join Ring to R and Tip to T you should get your phone line and the alarm disconnected. But you alarm may throw a wobbly if it detects that the phone line has been disconnected.
The British Gas alarm panels are normally DSC Envoy panels if that helps.