Queen Charlotte died nearly two centuries ago but is still celebrated in her namesake American city. When you drive from the airport in North Carolina, you can't miss the monumental bronze sculpture of the woman said to be Britain's first black queen, dramatically bent backwards as if blown by a jet engine. Downtown, there is another prominent sculpture of Queen Charlotte, in which she's walking with two dogs as if out for a stroll in 21st-century America.

Street after street is named after her, and Charlotte itself revels in the nickname the Queen City - even though, shortly after the city was named in her honour, the American War of Independence broke out, making her the queen of the enemy. And the city's art gallery, the Mint museum, holds a sumptuous 1762 portrait of Charlotte by the Scottish portrait painter Allan Ramsay, showing the Queen of England in regal robes aged 17, the year after she married George III.

Charlotte is intrigued by its namesake. Some Charlotteans even find her lovable. "We think your queen speaks to us on lots of levels," says Cheryl Palmer, director of education at the Mint museum. "As a woman, an immigrant, a person who may have had African forebears, botanist, a queen who opposed slavery - she speaks to Americans, especially in a city in the south like Charlotte that is trying to redefine itself."

Yet Charlotte (1744-1818) has much less resonance in the land where she was actually queen. If she is known at all here, it is from her depiction in Alan Bennett's play as the wife of "mad" King George III. We have forgotten or perhaps never knew that she founded Kew Gardens, that she bore 15 children (13 of whom survived to adulthood), and that she was a patron of the arts who may have commissioned Mozart.

Here, Charlotte is a woman who hasn't so much intrigued as been regularly damned. In the opening of Charles Dickens's A Tale of Two Cities she is dismissed in the second paragraph: "There was a king with a large jaw, and a queen with a plain face, on the throne of England." Historian John H Plumb described her as "plain and undesirable". Even her physician, Baron Christian Friedrich Stockmar, reportedly described the elderly queen as "small and crooked, with a true mulatto face".

"She was famously ugly," says Desmond Shawe-Taylor, surveyor of the Queen's pictures. "One courtier once said of Charlotte late in life: 'Her Majesty's ugliness has quite faded.' There was quite a miaow factor at court."

Charlotte's name was given to thoroughfares throughout Georgian Britain - most notably Charlotte Square in Edinburgh's New Town - but her lack of resonance and glamour in the minds of Londoners is typified by the fact that there is a little square in Bloomsbury called Queen's Square. In the middle is a sculpture of a queen. For much of the 19th century, the sculpture was thought to depict Queen Anne and, as a result, the square was known as Queen Anne's Square. Only later was it realised that the sculpture actually depicted Charlotte and the square renamed Queen Square.

Hold on, you might be saying. Britain has had a black queen? Did I miss something? Surely Helen Mirren played Charlotte in the film The Madness of King George and she was, last time I looked, white? Yet the theory that Queen Charlotte may have been black, albeit sketchy, is nonetheless one that is gaining currency.

If you google Queen Charlotte of Mecklenburg-Strelitz, you'll quickly come across a historian called Mario de Valdes y Cocom. He argues that her features, as seen in royal portraits, were conspicuously African, and contends that they were noted by numerous contemporaries. He claims that the queen, though German, was directly descended from a black branch of the Portuguese royal family, related to Margarita de Castro e Souza, a 15th-century Portuguese noblewoman nine generations removed, whose ancestry she traces from the 13th-century ruler Alfonso III and his lover Madragana, whom Valdes takes to have been a Moor and thus a black African.

It is a great "what if" of history. "If she was black," says the historian Kate Williams, "this raises a lot of important suggestions about not only our royal family but those of most of Europe, considering that Queen Victoria's descendants are spread across most of the royal families of Europe and beyond. If we class Charlotte as black, then ergo Queen Victoria and our entire royal family, [down] to Prince Harry, are also black ... a very interesting concept."

That said, Williams and many other historians are very sceptical about Valdes's theory. They argue the generational distance between Charlotte and her presumed African forebear is so great as to make the suggestion ridiculous. Furthermore, they say even the evidence that Madragana was black is thin.

But Valdes suggests that the way Queen Charlotte is depicted in Ramsay's 1762 portrait - which US artist Ken Aptekar is now using as the starting point for a new art project called Charlotte's Charlotte - supports the view she had African ancestors.

Valdes writes: "Artists of that period were expected to play down, soften or even obliterate undesirable features in a subject's face. [But] Sir Allan Ramsay was the artist responsible for the majority of the paintings of the queen, and his representations of her were the most decidedly African of all her portraits."

Valdes's suggestion is that Ramsay was an anti-slavery campaigner who would not have suppressed any "African characteristics" but perhaps might have stressed them for political reasons. "I can't see it to be honest," says Shawe-Taylor. "We've got a version of the same portrait. I look at it pretty often and it's never occurred to me that she's got African features of any kind. It sounds like the ancestry is there and it's not impossible it was reflected in her features, but I can't see it."

Is it possible that other portraitists of Queen Charlotte might have soft-pedalled her African features? "That makes much more sense. It's quite possible. The thing about Ramsay is that, unlike Reynolds and Gainsborough, who were quite imprecise in their portraits, he was a very accurate depicter of his subjects, so that if she looked slightly more African in his portraits than others, that might be because she was more well depicted. How can you tell? She's dead!"

Shawe-Taylor says that a more instructive source of images of Queen Charlotte might well be the many caricatures of her held at the British Museum. "None of them shows her as African, and you'd suspect they would if she was visibly of African descent. You'd expect they would have a field day if she was."

In fact, Charlotte may not have been our first black queen: there is another theory that suggests that Philippa of Hainault (1314-69), consort of Edward III and a woman who may have had African ancestry, holds that title.

As for Valdes, he turns out to be an independent historian of the African diaspora who has argued that Peter Ustinov, Heather Locklear, the Medicis, and the Vanderbilts have African ancestry. His theory about Charlotte even pops up on www.100greatblackbritons.com, where she appears alongside Mary Seacole, Shirley Bassey, Sir Trevor McDonald, Zadie Smith, Naomi Campbell and Baronness Scotland as one of our great Britons. Despite being thus feted, Charlotte has not yet had much attention, say, during the annual Black History week in Britain.

Perhaps she should get more. The suggestion that Queen Charlotte was black implies that her granddaughter (Queen Victoria) and her great-great-great-great-granddaughter (Queen Elizabeth II) had African forebears. Perhaps, instead of just being a boring bunch of semi-inbred white stiffs, our royal family becomes much more interesting. Maybe - and this is just a theory - the Windsors would do well to claim their African heritage: it might be a PR coup, one that would strengthen the bonds of our queen's beloved Commonwealth.

Or would our royal family be threatened if it were shown they had African forebears? "I don't think so at all. There would be no shame attached to it all," says the royal historian Hugo Vickers. "The theory does not impress me, but even if it were true, the whole thing would have been so diluted by this stage that it couldn't matter less to our royal family. It certainly wouldn't show that they are significantly black."

What's fascinating about Aptekar's project is that he started by conducting focus group meetings with people from Charlotte to find out what the Queen and her portrait meant to citizens of the US city. "I took my cues from the passionate responses of individuals whom I asked to help me understand what Queen Charlotte represents to them."

The resulting suite of paintings is a series of riffs on that Ramsay portrait of Charlotte. In one, a reworked portion of the portrait shows the queen's face overlaid with the words "Black White Other". Another Aptekar canvas features an even tighter close up, in which the queen's face is overlaid with the words "Oh Yeah She Is".

Among those who attended Aptekar's focus groups is congressman Mel Watt, one of very few African-Americans in the House of Representatives and who represents the 12th district of North Carolina which includes Charlotte. "In private conversations, African-Americans have always acknowledged and found a sense of pride in this 'secret'," says Watt. "It's great that this discussion can now come out of the closet into the public places of Charlotte, so we all can acknowledge and celebrate it."

What about the idea that she was an immigrant - a German teenager who had to make a new life in England in the late 18th century?

"We were a lot more immigrant-friendly in those days than we were friendly to people of colour," says Watt. "We all recognised that we all came from some place else. But there was always a sense of denial, even ostracism, about being black. Putting the history on top of the table should make for opportunities for provocative, healing conversations."

Does Valdes's theory conclusively determine that Queen Charlotte had African forebears? Hardly. And if she had African forebears, would that mean we could readily infer she was black? That, surely, depends on how we define what it is to be black. In the US, there was for many decades a much-derided "one-drop rule", whereby any white-looking person with any percentage of "black blood" was not regarded as being really white. Although now just a historical curio, it was controversially invoked recently by the African-American lawyer Alton Maddox Jr, who argued that under the one-drop rule, Barack Obama wouldn't be the first black president.

In an era of mixed-race celebrities such as Tiger Woods and Mariah Carey, and at a time when in the US, the UK and any other racially diverse countries mixed-raced relationships are common, this rule seems absurd. But without such a rule, how do we determine Charlotte's ethnicity? If she is black, aren't we all?

It's striking that on US and UK census forms, respondents are asked to choose their own race by ticking the box with which they most closely identify (though there can be problems with this: some people in Cornwall are angry that the 2011 census form will not allow them to self-define as Cornish because only 37,000 ticked that box in the 2001 census and that figure has been deemed too small to constitute a separate ethnic group). We will never know which box Queen Charlotte would have ticked, though we can take a good guess. But maybe that isn't the most important issue, anyway.

For congressman Watt's wife Eulada, along with some other African-Americans in Charlotte, the most important issue is what the possibility that Queen Charlotte was black may mean for people in the city now. "I believe African-American Charlotteans have always been proud of Queen Charlotte's heritage and acknowledge it with a smile and a wink," she says. "Many of us are now enjoying a bit of 'I told you so', now that the story is out."

But isn't her heritage too sketchy to be used to heal old wounds? "Hopefully, the sketchiness will inspire others to further research and documentation of our rich history. Knowing more about an old dead queen can play a part in reconciliation."

And if an old dead queen can help improve racial trust in an American city, perhaps she could do something similar over here. Whether she will, though, is much less certain.