The phrase buy me and stop one is a reversal of stop me and buy one, the slogan displayed on the box-tricycles that the vendors of Wall’s Ice Cream used to ride—cf. meaning and origin of the phrase ‘stop me and buy one’.

The phrase buy me and stop one has had a variety of applications, because a number of persons, independently from each other, coined it on various occasions and for different purposes.

In the 1970s, buy me and stop one was frequently found scrawled on contraceptive-vending devices in public conveniences—as mentioned in ‘Contraceptive machines in loos’ plan rejected, published in the Kensington Post (London, England) of Friday 16^th June 1972:

A move to have contraceptive machines installed in Westminster’s public conveniences was narrowly defeated at Monday’s City Council meeting.
The suggestion was made earlier this year by Councillor Jonah Walker-Smith […].
He told the meeting: “Whoever first wrote ‘buy me and stop one’ on one of these machines had a sense of responsibility as well as a sense of humour.
“There are far too many abortions, and far too many unwanted pregnancies, which result in children being taken into the council’s care.”
The machines would be used by the “faceless and promiscuous” who, although their activities were most likely to lead to unwanted pregnancies, would be the least likely to attend the council’s birth control clinics.
[&c.]

As applied to contraceptives, the phrase also occurs in Posters ‘are too shocking’, published in the Liverpool Echo (Liverpool, Merseyside, England) of Tuesday 23^rd July 1974:

Shock posters on family planning produced by a charity group for distribution in schools, clinics, and clubs, have come under fire from the Family Planning Association as “too outspoken.”
One poster shows several contraceptive devices and has the caption, “buy me and stop one.” Another reads, “no one says you shouldn’t do it” . . . and goes on to say, “sexual intercourse was designed to produce babies. Contraceptives are designed to prevent them.”
Another poster in the set of seven reads: “Make love not babies.”
But the FPA said of the posters—produced by the Hampshire group, Project Icarus—“They are using shock tactics and we feel their message is too outspoken for display in our clinics.”
The posters were not conservative enough for clinics where there was mixed company of all ages, said the FPA.
But the chairman of Project Icarus. Mr. Ian Dillow, said: “We think these posters have tremendous potential. They don’t preach, and they don’t threaten damnation.”

In the Daily Mirror (London, England) of Wednesday 2^nd December 1970, the columnist Christopher Ward claimed to have come up with the phrase buy me and stop one as applied to contraceptives:

They asked for it . .
I was invited last week to take part in a seminar held by that fine public body, the Family Planning Clinic.
Among the many subjects we discussed was the need to encourage responsible behaviour among young people through advertising.
One of the suggestions for a slogan to advertise contraceptives was, in my view, nothing less than brilliant, on account of the fact that I made it.
It was: Buy me and stop one.

But the phrase had occurred four decades earlier, in two drink advertisements:

1: An advertisement published in The Evening News (Portsmouth, Hampshire, England) of Tuesday 20^th May 1930:

Little Bricky says:
Have you a thirst?
BUY ME AND STOP ONE!
Sunshine Ale

2: An advertisement published in the Montrose Review, and Angus and Kincardine Shires Advertiser (Arbroath, Angus, Scotland) of Friday 11^th July 1930:

Have you a Thirst?
BUY ME AND STOP ONE.
ALEXANDER’S
PRIZE MEDAL WATERS
1927-1929.
BALTIC STREET, MONTROSE.

In the column From Here, There and Everywhere, published in The Wells Journal (Wells, Somerset, England) of Friday 4^th September 1931, it was probably because he was evoking ice cream that ‘the Looker-On’ altered the original advertising slogan stop me and buy one:

Cold Comfort.
I noticed that a defendant in a recent police court case stated that after he had been engaged in defending himself against the blows of a plaintiff he “went and had an ice cream.” In byegone days it was always suggested that we should count ten before we replied or retaliated in the event of an argument in which words or brute force were employed. It is now a question of “Buy me and stop one!”

In The Tatler (London, England) of Wednesday 17^th August 1932, the column Bubble and Squeak explicitly referred to the original advertising slogan:

Said Jones: “I heard of a clever man the other day.”
Said Smith: “Why, what did he do?”
Said Jones: “Well, he used to run an ice-cream van here with ‘Stop Me and Buy One,’ and now he’s gone over to Chicago and invented a patent bullet-proof waist-coat, and now he’s got a van with the words, ‘Buy Me and Stop One’!”

The phrase buy me and stop one was used as the caption to this cartoon inspired by Wall’s Ice Cream vendors, published in the Daily Herald (London, England) of Tuesday 18^th May 1943:

In this cartoon, Benito Mussolini¹ is taking out ice-cream bricks² from a box displaying the words “Bricks” and “Ice Cream Walls”, and is distributing those bricks to his soldiers, who are using them to build up futile defensive fortifications against “Allied Heat”, i.e., the bombs launched by the Allies³.

¹ The Italian Fascist politician Benito Amilcare Andrea Mussolini (1883–1945) was Prime Minister of Italy from 31^st October 1922 to 25^th July 1943.
² Among other products, Wall’s sold Standard Ice Cream Bricks.
³ The Allies had, on 14^th May 1943, bombed the port of Civitavecchia, 35 miles north-west of Rome.