I've watched 'Line of Duty' now so I'm backI think the whole ending was a set up for Season 7.
You're right. He shouldn't have diplomatic status but I can guarantee he will have. You only qualify for diplomatic immunity if you are working on behalf of the British Crown and he isn't. It will be one of those 'one rule for us' scenarios.
(By 'British Crown' I don't just mean the RF. Civil servants all over the world have diplomatic immunity.)
Its very curious to find Harry has it.
The only serving he does is self-serving.