These "unattributable assets" are in many countries' arsenals, including, of course, the UK.
In 1969 Henry Kissinger needed to get to Paris several times without much attention for secret talks with the Viet Cong. The French provided a Falcon 20 with a civil registration after being told of the urgent need for discreet transportation. Even the French were not aware of the real mission. "There is a woman involved" was the cover story given for the Secretary's travel requirements.
The UK used to operate a couple of Hawkers with civil registrations and murky missions. Presumably, these have been upgraded to something else.
The South Africans had a mysterious Cessna Citation operation that now seems to have been involved in nuke weapons "research" with Pakistan and Israel.
In recent years, a lot of covert aviation activity seems to cycle between contractors and military crews. The famous "Janet" flights from KLAS to Area 51 have at times been operated by contractors like Key Airlines. Now, I believe they are flown by Air Force pilots. Of course, this operation is well known to the locals and has even made the cover of National Geographic.