But the bizarre sight that awaited him was to make headlines around the world and cause a moral panic that led to the introduction of strict new censorship laws in the UK.
Hundreds of children aged from four to 14, some of them armed with knives and sharpened sticks, were patrolling inside the historic graveyard.
They were, they told the bemused constable, hunting a 7ft tall vampire with iron teeth who had already kidnapped and eaten two local boys.
Fear of the so-called Gorbals Vampire had spread to many of their parents, who begged Pc Deeprose for assurances there was no truth to the rumours.
Newspapers at the time reported that the headmaster of a nearby primary school told everyone present that the tale was ridiculous, and police were finally able to disperse the crowd.
But the armed mob of child vampire hunters was to return immediately after sunset the following night, and the night after that.
Urban Myth
Ronnie Sanderson, who was an eight-year-old schoolboy in the Gorbals area of the city when the vampire scare was at its height, described how Chinese whispers in the schoolyard escalated into full-blown panic.
He recalled: "It all started in the playground - the word was there was a vampire and everyone was going to head out there after school.
"At three o'clock the school emptied and everyone made a beeline for it. We sat there for ages on the wall waiting and waiting. I wouldn't go in because it was a bit scary for me.
"I think somebody saw someone wandering about and the cry went up: 'There's the vampire!'
"That was it - that was the word to get off that wall quick and get away from it.
"I just remember scampering home to my mother: 'What's the matter with you?' 'I've seen a vampire!' and I got a clout round the ear for my trouble. I didn't really know what a vampire was."
There were no records of any missing children in Glasgow at the time, and media reports of the incident began to search for the origins of the urban myth that had gripped the city.
The blame was quickly laid at the door of American comic books with chilling titles such as Tales From The Crypt and The Vault of Horror, whose graphic images of terrifying monsters were becoming increasingly popular among Scottish youngsters.
Corrupt comics
These comics, so the theory went, were corrupting the imaginations of children and inflaming them with fear of the unknown.
A few dissenting academics pointed out there was no mention of a creature matching the description of the Gorbals Vampire in any of these comics.
There was, however, a monster with iron teeth in the Bible (Daniel 7.7) and in a poem taught in local schools.
But their voices were drowned out in the media and political frenzy that was by now demanding action to be taken to prevent even more young minds from being "polluted" by the "terrifying and corrupt" comic books.
The government responded to the clamour by introducing the Children and Young Persons (Harmful Publications) Act 1955 which, for the first time, specifically banned the sale of magazines and comics portraying "incidents of a repulsive or horrible nature" to minors.
Another of those who had gathered at the graveyard as a child, Tam Smith, said the Necropolis provided the perfect stage for a vampire story to take root, with the noise and light from the nearby ironworks casting spooky shadows across the graves in which some 250,000 Glaswegians had been laid to rest.
Mr Smith said it had been common for naughty children in the area to be threatened with the Iron Man - a local equivalent of the Bogeyman - by their exasperated parents.
Holy Grail
Neither Mr Smith or Mr Sanderson had televisions in their homes at the time, and neither had ever seen a horror movie or read a horror comic.
Comic book expert Barry Forshaw said getting their hands on one of the underground American horror comics had been like finding the Holy Grail for schoolyards of British children reared on the squeaky clean fare found every week inside the Beano and Dandy - both of which are produced in Scotland.
The story of the Gorbals Vampire had been a gift to the unlikely alliance of teachers, communists and Christians who had their own individual reasons for crusading against the corrupting influence of American comics, he said.
Mr Forshaw added: "It was a perfect fit. Here was a campaign that was looking for things to justify itself, and then this event happens.
"It is ironic that the moral furore began in Scotland, where the comics could not have been more safe."
