In British English, jam butty, also jam sandwich, has been a colloquial appellation for a police patrol car having a red stripe painted on a white background—as explained by David Mills in Training police drivers, published in The Illustrated London News (London, England) of September 1983:

A police car in a hurry has always been an impressive sight. In the 1950s shiny black Wolseleys could be seen tearing along trunk roads. They were wireless cars, complete with a wireless operator versed in the art of radio telephony. In the 60s rounder, lower, more powerful S-type Jaguars hurtled along the new motorways, bells jingling the ordinary motorist out of the way. The 70s saw the emergence of the “jam sandwich”, a 150-horsepower Rover V8 saloon with flashing blue light sometimes set between two spotlamps on the roof. Villains took to calling this fast flyer a jam sandwich because it had white coachwork with a stripe running round the car at knee height which looked remarkably like a butter and jam filling.
In the 80s the Rover badge and jam filling remain, but on a hatchback saloon with fatter tyres that give excellent grip, and sports suspension to keep them glued to the road on the bumpiest corners. A modern police Rover can lap Brands Hatch only seconds slower than saloon racing cars.

Photograph by Richard Cooke, from Training police drivers, published in The Illustrated London News (London, England) of September 1983:

 

—Cf. also, in British English, panda, denoting a police patrol car having a broad white stripe painted on a dark background.

These are, in chronological order, the earliest occurrences that I have found of jam butty, also jam sandwich, applied to a police patrol car:

1-: From On the crime front—Not so many nasty little acts, published in the Coleshill Chronicle (Coleshill, Warwickshire, England) of Friday 23^rd July 1971:

The Motorway Patrol Group is now getting into its stride and certain locals have been heard describing these cars with the orange flash down the centre as ‘Jam Butties’. However, they are exceptionally well equipped and the crews capable of dealing with anything on their section of the Motorway.

2-: From the Liverpool Echo (Liverpool, Lancashire, England) of Monday 1^st November 1971:

Jam butty cars

A new name for the Cheshire police traffic cars is the jam butty cars.
It came about when a witness at Birkenhead Magistrates’ Court said: “We were standing there when the jam butty car came up.”
The Magistrates Clerk, Mr. John Cullen, queried the name and then said “I suppose that is to distinguish between the panda car * and the cream police car with the red stripe.”
“Yes sir,” replied the witness, a teenage youth.

* In British English, the noun panda has been a colloquial appellation for a police patrol car having a white stripe painted on a dark background.

3-: From the column Talking Point, by June Johns, published in the Cheshire Observer (Chester, Cheshire, England) of Friday 5^th May 1972:

Time was when a Bobby on the beat was in tune with his patch. He could ‘feel’ if something was amiss or if the villains were at work. In a car he is insulated from atmosphere and his personal antennae are out of action.
But a good policeman, like any artist or craftsman, relies on more than his hearing and his eyesight; he uses his extra senses—and time and time again they prove him right.
Getting fat behind the steering wheel is only one depressing result of the modern approach to crime, and I am not alone in calling for the return of the foot patrolman from whom good citizens can seek advice and whom criminals learn to fear.
The ‘jam-butty’ car of the traffic cop and the Panda of the suburbs are poor compensation. Until we get policemen silently patrolling the quieter areas of our city, none of us is free from the dangers of assault and robbery, dangers which, in 20^th century England, are totally unacceptable.

4-: From a letter to the Editor, by one Lionel James, published in The Central Somerset Gazette (Wells, Somerset, England) of Friday 14^th June 1974:

He said he were coming down over the hill t’other night from Hunters’ Lodge, and by Ash Lane he got quite confussed with they speed limits, 30 one side of the entrance to Ash Lane, 40 t’other side, straight across the Bristol Road and back into 30. I said that were crafty, but he gave I another word for it and reckoned any time now there’d be one of they jam sandwich police cars on permanent duty there—they’d do a roaring trade.

5-: From Waging war against the speedster, by Ken Sutton, published in the Cheshire Observer (Chester, Cheshire, England) of Friday 28^th March 1975:

The aggressive eager-beaver who makes things unpleasant and dangerous for other road users is really up against it when he tangles with VASCAR.
A police car with this little magic box can record the road hog’s speed whether the police car is stationary, travelling in front of him, behind him or even coming towards him.
VASCAR—vehicle average speed computer and recorder—consists of a box fitted to the dashboard of the car, a connection to the speedometer and mileometer cable and a computer under the front passenger seat. […]
[…]
[…] Chief Supt. McArdle, the traffic chief for the county, said that VASCAR equipment will be fixed in marked “jam butty” police cars for operational purposes.

6-: From a letter published in the Sunday People (London, England) of Sunday 20^th April 1975:

Because of their bold red-on-white stripes police patrol cars are known locally as “Jam butties.”
Following one last week I was amused to note the Cheshire registration letters were JMB. Coincidental, no doubt, but a status symbol that takes some beating.
—(Mrs.) B. Whitehead, Wirral, Merseyside.

7-: From the Somerset Standard (Frome, Somerset, England) of Friday 26^th November 1976:

It’s a testing time for the speed cops

Speed cop Ruben Borjesson has resigned from the police force again.
He does it every time he goes rallying outside his home country, Sweden. And he joins up again when he gets back.
It’s the only way he can compete in events like the Lombard RAC.
Borjesson, a 29-year-old patrol driver, and Bath Police detective Joe Hawkins will crew Jam Sandwich—a Group 1 BMW 320 which gets its nickname from its colours of white with a red stripe.
Apart from a brief trial in Australia it’s the first time that one of BMW’s 300 series has competed in any rally in the world.