US Forces in UK and Status of Forces Agreement
Brief details in this Parliamentary Paper here:
www.parliament.uk/briefing-papers/SN06808.pdf
which
inter alia:
....briefly examines the legal agreements governing the United States Visiting Force in the United Kingdom. The legal basis for the US Visiting Force in the United Kingdom is primarily the North Atlantic Treaty Organisation (NATO) Status of Forces Agreement of 1951 (SOFA) and the Visiting Forces Act of 1952.
If you serve/served in Germany you are/were covered by a similar SOFA with all the privileges it allowed, the main one I remember when I was there were the tax and duty-free petrol coupons, tax free shopping in the NAAFI etc.