@izzythepush,
It's more or less an identical situation here in Germany (but we have more than twice as much US-soldiers in Germany than are in the UK).
A special legal regime applies to criminal offences committed by US soldiers stationed in Germany; this is set out in the NATO Status of Forces Agreement and the associated supplementary agreement.
In principle, the US has primary jurisdiction over its soldiers if the offence is committed whilst on duty or is directed exclusively against US property or other US citizens.
In the case of offences committed off duty against German citizens, there is a situation of concurrent jurisdiction, in which Germany has waived its primary right to prosecute but may reclaim this right in individual cases (which very rarely is agreed by the US if at all).
High-profile local incidents have triggered intense public debate over whether Germany should retain custody.
