They called themselves the 'D-Day Dodgers' because they didn't take part in the Normandy landings of 1944, serving in Italy instead.
But did that mean they had an easy ride? God no.
Their ballad, sung to the tune of the contemporary song Lili Marlene, reflected a typically ironic outlook from British squaddies.
"We're the D-Day Dodgers, out in Italy
"Always on the vino, always on the spree.
"Eighth Army scroungers and their tanks,
"We live in Rome, among the Yanks.
"We are the D-Day Dodgers, over here in Italy."
The reality, of course, was that Italy was anything but a cushy sector.
It may have seemed that way when compared to the violence unfolding during and after D-Day, as the Allies had to fight tooth-and-claw to pincer the Third Reich.
In contrast, save for the harsh winter of Northern Italy leading to a pause in the fighting there, things went relatively well for the Allies in that area in late 1944 and early 1945.
But juxtaposing the way the remaining German resistance in Northern Italy broke down in 1945 with the war in Northern Europe is unfair.
The 'D-Day Dodgers' of the British Eighth Army had, along with their American (and other) allies, taken part in a 23-month campaign to roll up the Italian peninsula. The purpose? To draw German forces away from the Russians and France.
Having bested the Germans in Africa, the campaign began in July 1943 with a major airborne and amphibious assault on Sicily.
The fighting was difficult, and the Allies suffered 22,000 casualties - compared to 10,000 on D-Day.
After its capture, Sicily became a launch pad for the mainland. Once ashore, the Allies faced an uphill slog, literally in many instances, to push the German and fascist Italian forces up the peninsula.
Things looked promising early on. On 25 July Mussolini was deposed and, by early September, the new government formally surrendered to the Allies.
Unfortunately, the German forces in Italy didn't, and a series of battles ensued.
Salerno, on 9 September 1943, saw 70,000 Allied troops plunge into battle on the mainland. Naples was next, and it fell on 1 October. After that, the Allies had to pass through minefields and mountain passes that offered little or no cover.
By January 1944, the Allies had reached Cassino, where the American 34th Division suffered 80 per cent casualties as the Allies fought through the town. They were then confronted by a virtually impregnable monastery on a mountain filled with German troops. It took months of fighting, including bombing from the air, to get the mountain in Allied hands.
From there, it was on to Rome in June 1944, before fighting through the Gothic line, fighting that was stopped by the winter before recommencing in 2pring 1945.
By this time, Mussolini had been rescued on the orders of Hitler, with the intention that he would be installed as a dictator in the remaining Axis-held territory in Northern Italy. However, he was captured and killed by Italian partisans and his body hung ignominiously in Milan.
Churchill had conceived of the fighting in Africa and the subsequent Italian Campaign as a chance for the Allies to weaken the Axis powers by nibbling at the soft underbelly of a crocodile before striking its tough snout, the Atlantic Wall in northern France.
But in the end Operation Overlord, in Northern Europe, cost the Allied Powers about 225,000 casualties, while casualties in the Italian Campaign came to over 300,000.
So the glory of the Normandy landings and fighting in Northern Europe should not overshadow the hard work done by the Allies in Italy, even if the humour of the 'D-Day Dodgers' does suggest that they were a little modest about their contribution to the war effort.