A lot of British slang doesn't seem to make a lot of sense at face value, but there is always a reason for it. Terms like 'Chelsea tractor' or 'sleeping policeman' are examples that no Brit would blink an eye at, and alongside them sits the 'jam sandwich.'
Among the many key differences between American and European police cars, or in this instance, specifically British ones, is that police vehicles from a very specific era in Britain picked up the nickname 'jam sandwiches.' The reason is simple.
Prior to the jam sandwich design, but after the British asked racing drivers to coach police drivers in the '30s, most police vehicles were blue and white in design. Then, in the 1970s, a more recognizable design was introduced. These new police cars were white, or occasionally silver, with a fluorescent red-orange stripe down each side.
When passing at speed, a flash of white with a stripe of red in the middle would, apparently, look a little like a jam sandwich, albeit with the dimensions of a Rover SD1. The term quickly became ingrained into mainstream popular culture thanks to its use in various TV shows, although usage dropped out of daily chatter when the design was replaced with the yellow and blue squared 'Battenburg' design.
Britain has a history of somewhat disappointing police vehicles
Police vehicles have an important job, and at times, they need to be capable of performing at seriously high levels. A police chase is never going to end well if the offender has a faster car, so it stands to reason that most police forces have some impressive bits of kit in their vehicular arsenal.
Italy famously uses Lamborghinis in its police force, Dubai's police force boasts dream exotics like Bugattis and Ferraris, and America boasts models such as the SSP Mustangs and Dodge Charger Pursuit. Britain, on the other hand, sports a back catalog which includes diesel Vauxhall Astras, the remarkably unremarkable Proton Impian, and 1,098-cc-powered Austin A40s.
The iconic SD1 jam sandwich was arguably one of the most exciting cars ever used in British policing circles, boasting a naturally aspirated 3.5-liter V8. However, electrical woes and severe corrosion issues likely made them even less useful than the sub-50-horsepower Austins of the 1960s — themselves dubbed 'panda cars' due to their distinctive black and white livery. Some cool cars did make the cut, like the Lexus IS-F or final-generation Mitsubishi Lancer Evos, but very seldom were these spotted actually in use, if at all.