Cobham use the aircraft you captured to provide training for the UK military.
The designation Falcon 20EW indicates it is an electronic warfare aircraft as can be seen by the underwing electronic jamming chaff/flare dispenser pods.
They basically act as an target primarily for the air force and navy.
Often these Falcon jets will be seen accompanied by one or more Hawk or similar jet trainers that simulate sea skimming missiles for the navy.
This is along the same lines as ATAC in the US providing similar support.
Originally the were known as Flight Refuelling Limited (FRL).
Many countries use similar private enterprise organisations to provide training on an as needed basis.
Check wiki.
https://en.wikipedia.org/wiki/Cobham_plc
Because a business has some dodgy suspect companies or dodgy individuals as shareholders or bankers/financial advisor does not necessarily make the business dodgy.
The Rothschilds own or control just about every major financial services & banking organisation in the world, so to find them listed as having some link to the company is not surprising.