In peace time (or non operational circumstances) the MOD has a responsibility to investigate all incidents (including near misses). This is as a result of being an employer and therefore being subject to the Health and Safety at Work Act.
One of the reasons for the existence of the act is because of the human rights act and our right to life, i.e an employer has to do everything possible to preserve life, including not conducting an action if reasonable measures to preserve life cannot be implemented (hence risk assessments).
During combat operations the MOD are excused parts of the human rights act (granting them what is termed combat immunity) to enable the armed forces to function. This is the reason why we cannot sue the MOD for injuries in combat (negligence aside).
Accidents in peacetime are avoidable because parameters can be implemented to safeguard personnel. It is the LAIT's (and certain other agencies) job to investigate these incidents, ascertain the cause and make recommendations as required.
Near misses/close calls are a part of combat operations, if litigation cannot be raised for things that do happen on ops it certainly cannot be raised for things that don't happen. Therefore there's no need to investigate the incident.
Besides this there are the impracticalities of investigating an operational incident. Only deaths are investigated, this is not as a result of 'elf and safety, but because it remains statute the deaths and cause of deaths of all UK citizens is to be recorded.
In short, there is no requirement for investigations to happen, this may not seem ideal, but the purpose of the LAIT is to ensure we learn. On operations this is called experience, close calls should be covered in wash ups so the CoC can deal with them immediately. But that's about all you will get.