If he was in the military I presume military police has some jurisdiction.

I would also presume there's some mutual law where if a foreign military member is on another countries soil (if you're in the military you can't just go on holiday to a foreign country without extra paperwork) that allows counties to retain their military courts jurisdiction even on foreign soil.

That doesn't mean he gets off - just that the trial would be under US MP law. To be honest, the consequences of which would be higher for him than under UK law.

They already held the court martial. He got six months in prison. Way less than he'd have gotten under UK law.