Chris

It looks like it has a pair of odd screw heads in the centre to prevent tampering ... doubtless there's an expert on the forum somewhere who can name the type. Chances are you don't have the correct screwdriver or spanner to get them out, although I've found a pair of long-nose pliers is useful in many situations like this.

As spiderplant said the other day, it looks like it was a junction box for coaxial cable, which despite the BT logo suggests it was for TV, rather than telephone. I'd say it is very unlikely the cable that goes under your floor is attached to anything, but if you have your carpets up, there must be a trapdoor somewhere, for someone to have run the cable beneath the floor in the first place. If you're very curious, find that, get under the floor and see where it goes.

Once upon a time it would have found its way outdoors, and then on to a cable under your garden, to the street, and then a nearby cabinet on the pavement. The fact that there is a very old cut off wire on the other end of the box however suggests to me that there is basically no chance you're going to upset anything by removing it. If the cut end of cable was still attached to a TV distribution system it would probably have been causing interference all this time, and I would imagine would have been traced and dealt with.