It is not owned by Customer Service training nor has it ever been funded by that BA department. As you state it was used by Airport Operations Training for de-icing exercise with water and for tow-in push out for prospective aircraft tug drivers.
Due to its problems with regard to lack of maintainence TPS have been aware for the last few years that it required a new home. Irrespective of increased security it was also most unlikely that it would be available for open days etc.
Sadly unless some benefactor appears it will probably end up being broken up as I would guess it will be expensive to cut off the wings and move it that way.