US Borders in the U.K.
The major stumbling block for this will be firearms. The UK police & Border Force are not routinely armed, I can't see a foreign government's law enforcement officers carrying guns in the UK. I believe the only example of this is the Police Aux Frontieres in St Pancras, Stafford & Ashford who can travel on Eurostar with their guns but have store them when operating in the station. I can't see the Americans being so easily persuaded in handing there guns over to Border Force (Glasgow) or Police Scotland (on behalf of Border Force), although the US Sky Marshals already do so.