Another, HMS Ramillies, was already taking shape on the yard's slipway.
They were the events 100 years ago this week as the people of Glasgow and West of Scotland went about their business. But that year a global conflict was to begin that would see 200,000 men from the city go to war, 17,000 of them never to come back.
Yet the workers on the Clyde were busy making what amounted to the weapons of mass destruction of their age: the dreadnoughts were then most powerful battleships ever launched.
Benbow, Ramillies and the other dreadnoughts were being churned out on the Clyde, and not just for the Royal Navy.
Scottish yards were also arming Britain's future enemy, Turkey's Ottoman Empire.
The old pre-war Evening Times liked it that way - business, after all, for Clyde yards was good.Some politicians in London suggested slowing down the dreadnought programme, trying to find a way out of a costly arms race with Germany, Britain's maritime, military and economic rival.
In January 1914 we printed a cartoon. A haughty looking figure of Britannia, clutching a Trident, dismissed a kneeling figure called "Mr Littlenavy". "You have good intentions, no doubt," she told the top-hatted representative of the so-called Little Navy party. "But I won't trust my future welfare to your hands."
Most Scots, however, were giving little thought that the dreadnoughts would ever fire in anger.
The war scares of a few years earlier had diminished.
Conflict with Germany - which had just overtaken the United Kingdom as Europe's industrial powerhouse - looked less likely than in, say, 1912.
Yet the seeds of what was to become the Great War had already been sown by the end of January - 1000 miles from the growing carcass of the Ramillies in Dalmuir.
It was in southern France that a small group of Slav radicals - Serbs, Bosnians, Poles - met to plot the terrorist act that would propel Europe into a spiral that would end in conflict.
In the Hotel St Jerome, in Toulouse, at some point in late January the men decided to kill a prominent member of the ruling elite of Austro-Hungary as they fought to free Slav lands, such as makeup modern Bosnia and Herzegovina.
Eventually, one of the followers of the now notorious Black Hand group assassinated the heir to the Austrian throne, the Archduke Franz Ferdinand, as he visited Sarajevo.
The killing, by Gavrilo Princip, on June 28, 1914, was to lead to war within a month.
It is a century since that meeting in the Hotel St Jerome and still historians and politicians - especially in the UK - can't agree how it led to a war that cost 16million lives and ended in the redrawing of the map of Europe.
Europe in early 1914, however, was split into two armed camps that had very different loyalties in the Sarajevo assassination.
The first was dubbed the Central Powers. This was made up of Germany, bigger than it is now but lacking a significant overseas empire, and the Austro-Hungarian Empire, a huge expanse of much of central Europe. Its empire included the modern Czech and Slovak republics, Slovenia, Croatia, Hungary, Bosnia and parts of Romania and Poland.
This bloc initially included Italy - although it was to change sides - and later involved Turkey.
The second camp was the so-called the Triple Entente of the three huge empires of France, Russia and Britain.
Later, after hostilities broke out, Italy would join on the Allied side, Russia would drop out and, finally, America would back Britain and France.
This is often portrayed as a family dispute.
Historians still question how far supposedly ruling monarchs could control events in what Winston Churchill - who was First Lord Of The Admiralty as the dreadnoughts were being built on the Clyde - called the "old world in its sunset".
But Europe's rulers were individuals who knew each other intimately. Germany's Kaiser William II was first cousin to both King George V of Britain and Tsar Nicholas II of Russia.
Yet, despite good family relations, the rival camps eyed each other suspiciously in the decade before 1914.
In Britain, some recent histories have tried to blame Germany for allowing the war to develop.
This has been championed by UK Education Secretary Michael Gove, who likes to see the war as a conflict between western democracy and eastern despots, despite the fact that, in crude terms, Germany was a democracy and Russia, Britain's ally, was not.
P hillips O'Brien, an American who teaches history at Glasgow University, explained the recent controversy.
"The big question is whether the Germans are to blame or not, especially in the UK, where there is a school of thought that the war was about values."
In early 1914, as Glasgow workers laboured on the great ships of the coming Great War, such niceties would have meant little.
And the dreadnoughts at Beardmore's? They turned out to be needed.
The heavily armed Benbow played a key role in the biggest naval battle of the First World War, at Jutland, in 1916.
Ramillies joined the British Grand Fleet in 1917 and, despite her age, also saw much action in the Second World War.