I got lost somewhere there!
You've written "Despite having the phone and extension phone unplugged today at the landline point the phone rang", which doesn't seem to make sense to me. The phone ringing is triggered by a voltage passing along the telephone line. If the line's disconnected, the voltage can't pass along it; it's impossible!
Then you've written "Do we just to unplug the phone (having already taken out the phone line connections)". To me, if you've 'taken out the phone line connections', you've already unplugged it!
However, as long as you make sure that there's a break in the connection along the line somewhere (by unplugging whatever's needed to achieve that position), the phone can't possibly ring.
My own phone though has a switch underneath it for the ringer volume, which can be moved between 'high', 'low' and 'off'. (I always leave it in the 'off' position unless I'm expecting a call from someone on my landline).