MOD does not operate a licence scheme and all flying ops are conducted under a SofS derogation from the ANO. This means it is OK for a civilian without a licence to operate an MOD (military registered) aircraft provided the activity is managed and approved by MOD (via the Services or a contractor) and takes place under the derogation (iaw the MAA Regulatory Publications). However, you would expect the risk management process to require that instructors had an appropriate licence.
What is not OK is for a civilian to wear a flying badge indicating the attainment of certain standards and skills when they have not actually attained them.