Re: City of London Police = Rent-a-cop
For the Civil Nuclear Constabulary, anywhere near nuclear material is their patch. The Ministry of Defence Police jurisdiction is anything to do with the MoD ie employees equipment etc whether it is on MoD land or not.
The key phrase is "national police lead". The CoLP know more about complex fraud investigations so presumably other police services are happy to hand the investigation over to them rather than pull a couple of CID officers off a burgulary and tell them to start reading Stones.