The author of the article noted that the source of this story was somewhat dubious. It was first written by Gilbert Burnet, whose work also gave rise to some of the other myths of Henry's reign, and then ghoulishly embellished by Agnes Strickland in the Victorian era.
The king being carried to Windsor to be buried, stood all night among the broken walls of Sion, and there the leaden coffin being cleft by the shaking of the carriage, the pavement of the church was wetted with Henry's blood. In the morning came plumbers to solder the coffin, under whose feet — I tremble while I write it — was suddenly seen a dog creeping, and licking up the king's blood. If you ask me how I know this, I answer, William Greville, who could scarcely drive away the dog, told me, and so did the plumber also.”
It's probable elements of fiction got mixed into the tale, especially given its emotionally-satisfying and edifying morality tale ending, all tied up neatly in a supernatural bow with the ghostly dog.
But, as gross as it may be, it's highly probable Henry's coffin did leak, though I speculate that the "creeping" dog was probably an embellishment.
When Henry died on the 28th of January, the news was kept secret for several days while Edward Seymour, uncle of the minor prince who would inherit the throne, consolidated his power. Property and titles were parceled out to the other nobles on the council until they were satisfied and Seymour could ensure that his role of Lord Protector would be unchallenged.
Meals were delivered to the king's rooms as usual, and every appearance was kept up of the king being alive, but unwell.
On the 31st of January, the king's death was announced, and the embalmers were able to get to work. It was likely an unpleasant task. Henry was over 300 lbs. when he died and had infected leg wounds. He may have also been suffering from renal or kidney failure, which would have created a backup of fluid in his system. And, after three days, the natural process of decomposition would have set in.
Without getting too graphic, Henry's unembalmed body was probably already leaking. It's something that modern embalmers have to deal with in preparing remains, and in the modern era, bodies are usually chemically preserved within 24 hours of death when being prepared for a funeral.
Tudor embalmers would remove the intestines, heart and lungs. (This task usually fell to a noble's chandler, or the person who was in charge of the household's candles and wax, because wax was heavily used during the process.) Human decomposition usually begins within the stomach/intestines because of the natural bacteria already present. The removed organs would be casketed or put in urns, often buried at other churches that were important to the deceased, or along the road to their final funeral destination.
The body cavity was stuffed with sawdust, spices, and herbs. Sometimes wax was poured inside. The body would be rubbed with perfumed salves and ointments, then wrapped in cerecloth - a heavy, waxed, canvas-like material. The bundle would then be encased in sheets of lead by the household's plumber.
The lead coffin was put inside a more ornate outer coffin made of wood, often embellished with fine fabrics and gilded nails. Atop the coffin, an effigy of the deceased would lie. It was made from wood or wax, and meant to look as much like the deceased as possible. Sometimes, a "death mask" was used to create it. Grease would be smeared over the dead person's face, and then it was coated with wet plaster. Once it hardened, they had a perfect mold.
The effigy would wear the clothing of the deceased. Eyes open, sometimes smiling, it would stand in the place of the body, which wouldn't be quite so presentable for the long duration of the lying-in-state period or Tudor funerals, which usually lasted about a month.
It was likely because of the delay between Henry's death and embalming that his burial occurred a rapid two weeks after his death. The famous overnight stay at Syon Abbey occurred on February 14 - five years (minus one day) after the beheading of Katheryn Howard.
The story's narrative asserts that the jostling of the road had caused a separation in the plates of the lead coffin, which is certainly a reasonable explanation, but it may also be that the separation was caused by an explosion of decomposition gasses built up inside the lead coffin. As to why no one heard it? In the latter scenario, the excuse of the jostling might have been given because no one wanted to admit they'd left the coffin in the chapel alone overnight without attendants/mourners praying 'round the clock by the side of the dead king.
It's unlikely that the matter below Henry's coffin was actually blood. More likely, the fluids were the products of decomposition, and could have been tinted from the perfumes and spices used in the embalming procedure. The smell would have been ghastly. It is possible that it could have attracted an animal. In the Tudor era, strays often wandered in and out of buildings, feasting on scraps that were disposed of poorly in those days before proper sanitation. But my guess is that the dog was an embellishment by those who wanted to portray Henry as wicked, and deserving of a gruesome end.
According to the story, the plumber shored up the leaking inner lead coffin. Henry was transported another eight miles to St. George's Chapel, Windsor, where his body was placed in what was intended to be a temporary vault until his grandiose tomb could be constructed. That never happened, and there he remains.
He lay undisturbed next to Jane Seymour for a hundred years until his vault was opened to hastily admit the remains of Charles I after his execution. The location was more or less forgotten until the Victorian era.
The explorers noted that Henry's exterior wood coffin was in fragments, and the inner lead coffin appeared as though it had been "beaten in with violence about the middle." Henry's skeleton - including his skull, since "traces of beard" are mentioned - was actually visible, which means the lead plates must have completely peeled away, or gaped substantially. Jane Seymour's coffin, to Henry's right, was in perfect shape.
Some speculate the damage was actually done when Charles I's coffin was shoved into the vault. But a 1721 account of Charles' burial says that a footsoldier had crept into Henry's vault before Charles was placed in side and had stolen one of Henry's bones by reaching through a hole in the coffin beneath the pall* that lay atop.(The fellow had intended to use it to fashion a knife handle.) So it appears the damage had already been done.
If the reason why Henry's coffin leaked was due to an explosion of decomposition gas, the force could have damaged his exterior coffin. The damage wouldn't have been immediately noticeable to onlookers, because it would have been hidden below the effigy and the fabric palls laid over the lid. Or, the damage could have been caused by the plumber, who had to open the exterior wood coffin to solder up the leaking lead plates. It could also have happened after its internment in the vault.
Considering the delay between death and embalming, I would say that some leakage of the coffin was more likely than not. Whether it was enough to pool below on the floor is another matter. And due to the damage on Henry's coffin itself, I'm pretty confident that there was an explosion of decomposition gasses, either before his funeral or after it was placed in the vault.
*The palls that had been described in the 1721 description appear to have vanished by 1813, because the description of the interior doesn't mention them, nor does the examination and sketch done in 1888.