Gender variance and same-sex desire has always existed, in all times and in all places.

For many people, me included, this is a given. LGBT people didn't magically shimmy over the rainbow in 1967 when Lord Wolfenden's findings were finally put on the statute books. But for others, the thought of homosexuality and a spectrum of gender identity that is natural is enough to make them clutch feverishly at their pearls.

So let me take them on a tour around the British Museum and explore the theme of same-sex desire and gender through the objects displayed there, and perhaps buy them a copy of the book A Little Gay History: Desire and Diversity Across the World, by Richard B Parkinson. Those objects date back more than 2,500 years.

Let me show them the fragment of ceramic depicting the epic poem of Gilgamesh, a mythical king in ancient Mesopotamia who defeats the goddess Ishtar but loses his male lover and spends the rest of his days grieving while trying to outwit Death itself. It is as powerful a tale as any by Homer, as well as being one of the earliest examples of literature. And speaking of the unspeakable vice of the Greeks, the Warren cup, as well as being a sublime objet d'art, may bring a smile to the face of anyone who remembers the dinner scene in the 1996 film The Birdcage.

Nearby, two small gold coins portray Sappho, Greek poetess and resident of the island of Lesbos. Surprisingly few people know of the Roman emperor Hadrian's love for a beautiful young Greek boy, Antinous, yet he had dozens of statues put up in his honour after the young man drowned in the Nile, one of which is in the museum. And in Polynesia, same-sex acts were tolerated between gender-crossing males and socially initiated men. They may even have had a cultural "third" sex. An exquisitely decorated Maori treasure box provides evidence.

Then there are the stunning statuettes and idols from the Middle East and India. The voluptuous Hindu deity Lakshminarayan; the Mesopotamian deity known as "the Queen of the Night", depicted in a plaque; even Shiva – all have varying degrees of cross-gender association. All are ancient. Native Americans are widely known to have a third gender, and the British Museum holds an image of a winkte (translated from the Dakota language as "wants to be a woman"). Still not convinced? Then take a look at the same-sex erotica from 18th-century Japan, or the ornate quilt made by Pakistani hijras (trans women).

And what of society's changing attitudes towards homosexuality? A Dutch broadside from 1760 depicts the execution of 75 "sodomites". In Britain, where for years "sodomy" was a capital offence, fame and achievement were no protection from unjust laws. Oscar Wilde and Alan Turing were not the only talented men ruined for loving differently. In the museum is a letter to William John Bankes MP, whose discovery of an obelisk in 1815 played a significant role in the decipherment of hieroglyphs. He was later tried twice for indecency "against the order of nature", and died in exile in 1855.

Thankfully we can move on to David Hockney's print of two men in bed to accompany a poem by CP Cavafy, one of the earliest modern authors to write openly about same-sex love.

Which brings me to one last piece – a tiny one, but significant. A badge. A small triangular piece of metal imprinted with the words "LGBT History Month 2010". We arrive near the end: civil partnerships; (nearly) equal marriage; adoption rights; and workplace rights. Despite the efforts of our opponents (whose current evangelism is a measure that progress is still being made), we are tolerated and have recourse in law to open discrimination.

But until we are accepted in a society where being LGBT is usual and normal, where we can celebrate our identity every day, not just in February, then the journey is not over. And while there are people who need to see these magnificent objects in the museum, it cannot be over. So next year, we at LGBT History Month celebrate three geniuses under the curriculum-linked theme of music – Benjamin Britten, suffragette and composer Ethel Smyth, and the American "empress of the blues", Bessie Smith.

So repeat after me – gender variance and same-sex desire has always existed, in all times and in all places.