You almost certainly had a faulty brake master cylinder, but since the car has been scrapped, we'll never know for sure. You did the right thing in attempting to stop by using the handbrake: this will not cause a spin unless you were doing something stupid like still driving the front wheels or trying to do a boy racer handbrake turn; or as in the case of some Citroens, the handbrake operates the front wheels rather than the rear.
The handbrake isn't meant to provide braking ability for a moving vehicle, it's meant to keep a stationary vehicle from moving off unintentionally. The handbrake warning light warned you to put the handbrake fully down, and you did, therefore the light was doing its job.
The stuff you've read about brake fluid boiling and causing brake fade is IMHO a red herring in this instance. If you were driving hard, repeatedly braking fiercely for bends etc, or towing a loaded trailer down a bendy winding hill, then maybe, but nothing in your posts suggests this may be relevant.
Steve