Encorebaby.. . .
You say you were given a steer, was the traffic at 5 miles when steered or was the traffic on your course some time after the steer?
Your cleared altitude, was that something that the unit gave just prior or was it a level co-ordinated many miles ago as a release level from CAS?
You say that ATC did nothing , well if you had traffic on the nose at the same level at 5 miles then why have you not mentioned a TCAS TA or even an RA? The absence of both would indicate that ATC actually did do some thing and perhaps vectored around said traffic!
The controller had also explained that the traffic was military traffic manoeuvring up and down rapidly
SO it was manoeuvring traffic - that normally involves rapid changes in heading and level . . . .so maybe it was that traffic that flew into conflict with you and not you turning into conflict with that traffic which if manoeuvring would have been VFR / VMC.
Sounds to me like a routine encounter in class G airspace resolved by the controller actions "not reported by Encorebaby" or else we would all be sat reading transcripts in the UKAB!
One final point . . . . if you had asked for a Deconfliction Service, is your knowledge of the Pilots Obligations in the contract of agreement between controller and pilot actually good enough. For sure in the UK all controllers are well versed in their responsibilities, unfortunately the same could not be said for some of the airborne recipients! Just my views from the side-lines