The hero of the Armada died of dysentery in 1596, and his body - in a full suit of armour and lead-lined coffin - is known to have been laid to rest near the ships, which were scuttled shortly afterwards to prevent them falling into Spanish hands.

The Sunday Telegraph was granted exclusive access to the mission that is being conducted from the aptly-named Pirate's Cove by Deeptrek, a British-run subsea exploration company, working for the site's permit holder, IMDI Eco Olas.

Off a coastline of sheltered bays and malarial jungle, the waters here once teemed with Spanish and British fleets and pirates and privateers, all fighting for a share of plunder from the treasures of the New World.

So it is a thrilling sensation to look through a diving mask at what is very probably English oak hammered together in an Elizabethan shipyard in the late 1500s, at the height of the Crown's battles for maritime supremacy with Spain.

"To find two such vessels is very special," said James Sinclair, the team's marine archaeologist, as we bobbed above the wrecks between a rocky outcrop and headland long denoted on maps as Drake's Island and Drake's Point.

"And if as seems very likely these are confirmed as Drake's vessels, it will be a huge breakthrough for the world of maritime history and underwater archaeology."

Mr Sinclair was the first archaeologist to explore the wreck of the Titanic, but for him the current project surpasses the excitement of even that.

"The find here in Panama is a bit like a time travel," he said. "Once you have donned your scuba gear, you plunge not only through the water but through time and, if your imagination is keen, you find yourself in the hold of a sailing vessel from long ago.

"I have been one of the lucky people to push back that veil of time just a little and peer into the past. We are just starting to scratch the surface of one of the richest maritime areas for historical shipwrecks in the world."

Deeptrek is exploring several wreck-rich sites under contract to IMDI Eco Olas, which was issued with exploration permits by the Panamanian government. Funding has come from Panama, Australia and America.

In a wide-brimmed straw hat, Jay Usher, the company's Liverpudlian president, powered a speedboat towards the wreck site through the sticky tropical heat last week.

"What we're discovering out here already is incredibly exciting," he said. "And if we could locate and map Drake's coffin, then for a lad from Liverpool who did his first commercial dive in the Mersey, that really would be thrilling."

Mindful of sensitivities about maritime graves and wrecks, Mr Usher makes clear, however, that there would no "Arise, Sir Francis" moment.

"We have no intention of doing anything to disturb his grave or raising the coffin," he said. "It would be for the Panamanian authorities, in consultation with the British government, to decide what to do if we find the site.

"We are not treasure hunters. We are conducting a scientific research mission under licence to the Panamanian permit-holders and government."

There is compelling evidence that the wrecks are the remains of theElizabeth and the Delight, the vessels on Drake's last voyage to the New World.

In London, Trevor McEniry, a historical researcher hired by Pat Croce - the former owner of the Philadelphia 76ers basketball team turned pirate enthusiast, had done the initial detective legwork. He trawled through archives, journals and maps to pinpoint a grid to search for the wrecks and the coffin.

Tropical diseases had cut a lethal swathe through Drake's crews in 1596, meaning there was not enough manpower to continue with the full fleet. So the decision was taken to empty, torch and scuttle two ships just off the coast here.

Such was the hatred of the Spanish instilled by Drake that the vessels were meticulously stripped and then destroyed to avoid anything falling into enemy hands.

And as Mr Sinclair demonstrated by diving down to the seafloor to rub sediment from the remains, the timber fragments of these newly-charted wrecks are scorched black - in keeping with the how the missing vessels were burned after they were run aground in shallow water.

Earthenware recovered from the site, as well as the dowels and nailholes used in the ship-making process, are all indicative of that period. And of course the cartographical clues – the wrecks lie off Drake's Point, near Drake's Island – are also clear, but it will require further testing and dating of the remains for confirmation.

Drake himself had died from dysentry shortly before the vessels were scuttled on this last ill-fated mission. He was buried at sea in his armour, according to his wishes, in a lead coffin (thought by Mr Sinclair to be constructed of the lead-lined wood used to make ships of that era) and laid to rest "under the rock", according to one journal – very possibly a reference to Drake's Island.

He had been variously a naval captain, privateer, slaver and explorer. He circumnavigated the world from 1577 to 1580 in the Golden Hind, was knighted by Elizabeth I in 1581 and served as vice-admiral of the English fleet in the Spanish Armada in 1588 when his tactics of dispatching burning "fireships" into enemy lines played a key role in the victory.

For those legendary exploits, he was a hero to the English. But his raids on King Philip II's fleets and the sacking of his ports in the New World made him a pirate in the eyes of Spaniards, to whom he was known as el Draque (the Dragon), the Spanish pronunciation of his name.

The lure of Portobelo Bay for Drake was the treasure ships carrying gold, silver and emeralds back to the Old World from the magnificent natural harbour. With twin forts on the headlands, it was one of the most important ports in the Spanish Main.

That is difficult to imagine now. The town is an impoverished Caribbean backwater, although the harbour and cove still attract foreign seafarers, from wealthy American and European yacht-owners to drug-runners from neighbouring Columbia.

In the late 1500s, however, the customs house there was so crammed with precious metals and jewels thatsilver would be piled up in the streets until it was loaded on to the vessels. It was little wonder that Drake referred to the coast here as "the treasure house of the world".

The Deeptrek team also showed The Sunday Telegraph other period artifacts from a nearby site – including a conquistador's armour, axes, cannons and cannonballs dating back to shortly after Columbus.

These are destined for museum collections in Panama while IMDI intends to turn the presumed Drake wrecks into an international study centre.

"This is an incredibly exciting discovery for the people of Panama and the world," said Ernesto Cordovez, president of IMDI. "We think that can become an academic programme for students specialising in maritime subjects. It will be a great project for us."

Still missing is any sign of Drake himself, whom several previous searches have failed to locate.

But with the benefit cutting-edge mapping, sonar, remote sensing and subsea camera technology supplied by UK-based firms Seatronics and Bowtech, the 415-year-old mystery may finally be coming to a close.