Once you've absorbed all these images, a composite picture begins to form in the mind. It might not help your personal idea of the queen - which might well be Elizabeth Taylor or Claudette Colbert in the film role - but in my mind, Cleo is remarkably like Maria Callas. A jolie-laide, prone to weight gain and mood swings, who could look both ravishing and terrible, who went heavy on the eyeliner, who was bewitching company, who could play powerful men off against each other, who was routinely described as "divine", who was always in the news. Who became a legend.

The new exhibition at the British Museum, "Cleopatra of Egypt: from history to myth" rather skates over the matter of how she looked - though the accompanying book tackles the subject in some depth. A row of carved images in the show, for instance, presents us with various versions, variously attributed with greater or less certainty as being of the Queen herself, and including some imposing black basalt statues. What the curators choose instead to dwell on is the history of the Ptolemies, starting with Alexander the Great's conquest of Egypt, and setting their subsequent history within the political struggles of the time in the Mediterranean. Which essentially means the decline of Greece, the rise of Rome, and the way Egypt had to steer a course between rival power groups - at one point, for instance, being uncomfortably squashed between the rival empires of Rome and Carthage. By the time Cleopatra came on the scene, her empire was in serious decline.

So there is more history than myth here, since it aims to present, so far as possible, the real events underlying the great story, and which ends with the humiliation of Egypt by Rome. This is conveyed somewhat confusingly. The exhibition feels cluttered, squeezed as it is into the new Joseph Hotung gallery. This is the crescent-shaped space tucked behind the Round Reading Room as part of the Norman Foster/Spencer de Grey re-ordering of the BM's Great Court. Thus separated from the main Egyptian galleries, it has a force of its own, but this is an object-rich show which feels like it needs a lot more room in order to tackle the non-object stuff. Particularly when it comes to the Cleo myth, which is relegated to the backdrop. You find yourself longing nostalgically for an old-fashioned, logical rectangular gallery. This show needs more and better space in order to expand its themes.

The matter of Cleo's sex appeal and how she used it is beyond important, is inextricably bound up with the politics of the time and the region, just as it was for Elizabeth I of England. Cleopatra was chancing it at first by ruling solo rather than with her younger brother as tradition dictated, and early in her reign had to flee Alexandria as the said brother, then 15, ousted her. A stand-off ensued and a battle between the siblings' rival armies was about to commence when the Romans, as usual, arrived: Caesar had defeated the rebellious Pompey who had fled to Alexandria. Young Ptolemy saw to it that the luckless Pompey was killed, and presented Caesar with his pickled head. Good strategic planning: but Cleo saw her chance and went one better than her brother. This was when, according to legend, she showed the first signs of her postively Callas-like line in charismatic acting. She smuggled herself into the palace rolled in a carpet (actually a bed-linen sack, according to Plutarch), presented herself to Caesar, and got herself both reinstated on the throne and pregnant. Bearing Caesar's son, making this rather obvious by naming him Ptolemy Caesarion, and declaring him joint monarch aged three, was even smarter strategic planning. A shame, then, that Caesar had to go and get himself assassinated back in Rome.

Cleo had to start again. With Mark Anthony, the general who defeated Caesar's assassins and rivals and took over the Eastern Mediterranean, she thought up a better thespian wheeze than arriving in a linen sack. For that all-important first date, summoned to Tarsus by the new boss, she dolled herself up as a goddess and arrived by glittering ceremonial barge. Mark Anthony, who had goggled at her previously as an underling to Caesar in Alexandria, didn't stand a chance. Cleo got her man, and kept her throne. And when their twin son and daughter were born, was it not just a little showy to name them Alexander Sun and Cleopatra Moon (Helios and Semele, not names previously encountered in the Ptolemaic family tree)? Wow. Cleo was by now 27 and one hell of a star.