Jack Leslau, an amateur historian, believes that the boy princes were not murdered by their wicked uncle, Richard III, as recorded by Shakespeare, but were smuggled out of the Tower and grew up in Tudor England under false identities. One, Richard, Duke of York, he says, is buried in Belgium; the other, who reigned briefly as Edward V, in Chelsea.
Mr Leslau, who has spent 18 years and thousands of pounds constructing his theory, has been given permission by the Archbishop of Marines-Brussels to pass an endoscope, a flexible viewing tube, into a concealed chamber in the vaults of St Romuldus Cathedral in Mecklen, to discover whether it is the resting place of one of the princes. Scientists at the University of Louvain have agreed to carry out DNA profiling of the body within.
Mr Leslau believes that the princes became distinguished adults in the reign of Henry VIII and their true identities were kept secret. The elder of the two, Edward V, took the guise of Sir Edward Guildford, he says, and was passed off as the eldest son of Sir Richard Guildford, Comptroller to the Royal Household, while the younger prince, Richard, Duke of York, re-appeared as Dr John Clement, who qualified as a doctor, became president of the Royal College of Physicians and married the adopted daughter of Sir Thomas More, Margaret Gigs. He fled, like many other Catholic members of the gentry, to the Continent to escape the Protestant Reformation, and died in his nineties.
"I do not agree with the conventional story that Richard III murdered the Princes in the Tower," said Mr Leslau, a former jeweller from Kingsbury, north-west London. "I have been studying this problem for 18 years and I am convinced that the conventional theory is not right."
After researching his ideas with historians, scientists and doctors in the US and the former Soviet Union, he says there is no conclusive evidence to show that the two princes - sons of Edward IV - were murdered when they disappeared from the Tower of London in 1483 at the ages of 14 and nine.
One hundred and ninety one years later, in 1674, workmen discovered two skeletons in the Tower and it was assumed that they were of the missing princes. Although the remains were removed to be buried in Westminster Abbey, there was no proof that they were of the two princes.
Historians base their assumptions about the killing of the princes on Sir Thomas More's book, The History of King Richard III, but, said Mr Leslau, Sir Thomas had good reasons to vilify Richard, not least because he was a Yorkist and More was serving a Tudor king, who was descended from the Lancastrians. He also cites as evidence the fact that their mother, Elizabeth Woodville, at no point refers to their death or disappearance and remained on good terms with Richard III, their alleged murderer, who was her brother-in-law.
Now Mr Leslau's controversial theories are to be put to the test. He is planning to compare the DNA of Dr John Clement, who is buried in Mecklen, with that of Sir Edward Guildford, who, he claims, is buried in Chelsea Old Church, to see if they are brothers. If they are, he says, it will prove they are the missing princes. Then he hopes to get permission to test the DNA of Edward IV, their supposed father, wbo is buried at Windsor. But that would be the last step in the chain, because of the problem of winning the authorities' agreement.
It has taken Mr Leslau four years to clear the first hurdle of DNA testing, by getting permission to investigate the tomb in St Romuldus Cathedral. If the endoscope reveals two lead coffins, as Mr Leslau thinks it will, he hopes he will get permission to remove the wall to the tomb itself and test the body.
He also intends to investigate the tomb of Winifred and William Rastell, who were John Clement's daughter and Sir Thomas More's nephew and publisher. Their tomb is in St Peter's Church, Louvain, near Brussels. He is hoping that the DNA from Clement's daughter will help to prove his case and that, in excavating the tomb, they might find some of More's original manuscripts. These important historical documents, including The History of Richard III, have never been found. "We are assuming that they were not destroyed because they would have been too valuable," said Mr Leslau.
"We know from scanning the tomb, which is beneath a tiled floor in the church and which we discovered by using geo-radar, that it contains a shelf. We hope we may find some manuscripts on that shelf."
Mr Leslau, who is 64 and retired from his family jewellery business in 1981, knows that some people regard his ideas as far-fetched but is absolutely convinced of their veracity. His campaign to persuade the church authorities to let him try to obtain proof was helped by the recent showing on Belgian television of a film on his ideas.
One of Mr Leslau's main reasons for believing that Dr Clement was, in actual fact, the Duke of York, was the way in which this obscure doctor rose from nowhere, very rapidly, to become the president of the Royal College of Physicians.
"This position was in the gift of the King, and in the entire history of the Royal College, from the time the Letters Patent were granted in 1518 to the present day, Dr Clement is the only president for whom no records, portraits or signature remain and about whose family nothing is known."
Support for Mr Leslau's theory comes from the former Harveian librarian at the Royal College, Sir Gordon Wostenholme, who agrees that it is surprising the way that Clement was elevated to a very senior position at the college, only two months after he was made a Fellow.
"We have a proposal by Jack Leslau, with so much supporting evidence - all tiny pieces for the most part and nothing so convincing that everybody would have to accept the situation - that the sum total of these oddities makes the opposite argument extremely difficult," Sir Gordon said.
Apart from Clement's mysterious background, Mr Leslau relies for his evidence upon a portrait of the More family attributed to Hans Holbein, in which Dr Clement is shown in the doorway.
He thinks that Holbein knew Clement's real identity and left dozens of clues in the picture to inform future generations. He claims to have broken the painter's hidden code. The "clues" include Clement's position in the picture, which is higher than the others, the royal fleur-de-lis above his head and the words above him in Latin, saying: "John, the rightful heir".
"After spending days trying to crack the code, the message eventually jumped out. It is the best-fit hypothesis of what really happened to the princes because it takes into account every piece of known evidence, both positive and negative, from the period," said Mr Leslau, who is convinced that science will prove him right and his critics wrong.
One such critic is the historian, AJ Pollard, who claims in his book, Richard III and the Princes in the Tower, that Mr Leslau does not have "a shred of external or forensic evidence for his theories". Until he has evidence, his belief must remain "a brilliant flight of fancy".