Today is St George's Day and Shakespeare's birthday. Both symbolise a global and expansive sensibility and rebut those other characteristics one associates with England – twitchiness, arrogance, snobbery and supremacy. St George's mother was from Syria or Palestine, his father was Roman. Shakespeare, who married a local Warwickshire woman, wrote so perceptively and eloquently about cross-cultural and interracial relationships that no playwright since has ever come near.

I talk about those plays on BBC Radio 3 this Friday, as part of a series on the Bard and love. The times he lived in were raucous, adventurous, exploratory. Ships were sailing off to unknown places, bringing back fabulous new delights and stories. And dark strangers were arriving on these shores.

Queen Elizabeth 1 enthusiastically welcomed Muslim ambassadors and traders, loved their style. She could also be a dreadful racist – a contradiction one finds in England today. Black men were around then – slaves, performers, chancers – enough to set the Queen's teeth on edge. She tried to banish them but her people ignored her, some unable to resist black flesh.

One George Best wrote in his diary in 1578: "I myself have seen an Ethiopian, as blacke as a cole, brought into Englande, who taking a fair Englishe woman to wife begatte a sonne in all respects as blacke as the father was." Shakespeare truly understood such transgressive love, the audacity (and thoughtlessness too) of defiant couples crossing borders, provoking the rage of bitterly divided clans, nations and other hoarders of hostilities.

Eschewing blithe romanticism, he depicted moral ambivalence even in The Merchant of Venice, the one play where illicit love wins. Yes, we are with the rebellious lovers but with wild desires come warnings, unheeded warnings. In conflict zones – Bosnia, Palestine, Kashmir – they perform Romeo and Juliet, to divest themselves of inherited hate, the worst sort.

The Royal Shakespeare Company is about to stage a Shia/Sunni version from Baghdad. In one adaptation I saw a British Pakistani Juliet and Somali Romeo, both Muslims, divided by race. A troop of excitable Asian girls near me said they would be killed if they ever had black boyfriends. In Titus Andronicus, Tamora, the Goth Queen, has a secret lover, devious Aaron, a Moor. Bassiano, the Roman, scorns her: "Dost thou make your honour of his body's hue?" A child is born, a child Tamora wants murdered. Aaron snatches the baby and proclaims his blackness: "Coal-black is better than another hue, In that it scorns to bear another hue." Princess Diana's lover was the son of a merchant of Cairo, hated by the establishment. Rumours flew then that she was pregnant. If she had borne a dark baby, imagine the furore – and Dodi Al Fayed feeling the rage of Aaron.

With Othello, life has not only reflected the play but often overwhelmed it. In 1930 Paul Robeson played Othello and Peggy Ashcroft Desdemona at the Savoy Theatre. Critics were repulsed. More scandalously still, the stars were actually having a passionate affair. Robeson was defiant: "I am killing two birds with one stone. I am acting and I am talking for the negro as only Shakespeare can." As only Shakespeare can.

During the 1995 murder trial of OJ Simpson, the sub-text was clear. Here was a savage pretending to be civilised, just like Othello. Both seduced white women who ended up dead. Simpson was acquitted but never forgiven. Controversially Othello is today seen as a black man on the make. Too many still are, says Belinda, a black British designer: "They get white wives, passports to whiteland. No self-respect, they're still slaves."

Vile old Venetian prejudices now burn in the hearts of strong black women like Belinda. In The Merchant of Venice, Biblical animus pumps through the veins of the mercantile city. Shylock's daughter, Jessica, surrenders her faith and people, feels some shame but hopes that "I shall be saved by my husband. He hath made me a Christian" and Lancelot – the servant – ridicules her. It is a very Shakespearean interrogation of religious complacency.

The play was written two years after Rodrigo Lopez, the Queen's physician, was hanged for plotting to assassinate her, a false charge many believe. Lopez was a Converso, a Jew turned Christian for an easier life. Does Jessica give up Judaism for an easier life? These days many cross-religious couples choose one faith to live by. Muslims usually take possession of the non-Muslim partner. Catholicism is just as greedy, just as uncompromising. Gods are betrayed in the name of love or for an easy life.

In Antony and Cleopatra, assimilation is not a demand but an irresistible force. Mark Antony, colossus of the Roman Imperium, goes native. "Let Rome in Tiber melt and the wide arch of the ranged empire fall. Here is my space." It's a culture war and the orient wins.

You still find Britons turned Easterners, addicted to their wily Cleopatras and louche lifestyles. I met several on recent trips to Egypt, Jordan and India.

Of all the tribes of Europe, England is the most promiscuous, culturally and carnally and has been since it began to take shape. Scotland and Wales, in contrast, are more protectionist and relatively insular. I hope the English raise good cheer to that England today and its greatest son, Will.

Yasmin Alibhai-Brown's 'Shakespeare and Love' is 'The Essay' on Radio 3 on Friday at 10.45pm

y.alibhai-brown@independent.co.uk