I'm sure the BAe-125 is being used because it is cheaper, easily available, and works well in this role. If it is not available, another type would be used.
BBC has footage from someone who walked around with a camera:
https://www.bbc.co.uk/news/av/world-...ighway-landing
Most of the cockpit section seems to be entirely missing - would it be expected to burn up this quickly leaving so little behind?