Squeezing into a small room filled with half a dozen Indian eunuchs – and the Hollywood star Rupert Everett – I was mostly worried about treading on their beautiful saris. These are people one doesn’t want to offend. Rupert, splendidly bearded and in jeans, jumped right in and cheekily asked the chief eunuch, “How many of these girls still have their dicks?”

Halfway through filming a documentary about the great Victorian explorer Captain Sir Richard Burton, Rupert and I (as director) were trying to imagine his methods of social and sexual investigation. Burton was more than the explorer who famously failed to find the source of the Nile. He was fascinated by sex. He scandalised Victorian Britain not only by translating and publishing the great erotic texts of the East – the Kama Sutra, The Arabian Nights and The Perfumed Garden – but also by revealing the most intimate details of how people really lived and loved.

If Burton explored the world of brothels and massage parlours, dancing girls and eunuchs, often in disguise – and in danger – then, in the spirit of inquiry, so would Rupert.

We spent the day with a close-knit group of hijras in a poor district of Bombay. Most of these hijras are eunuchs; those that haven’t yet had the snip intend to follow suit. A marginalised community, they make a living by aggressive begging, dancing at weddings and prostitution. Burton found them compelling, and so did we. Gori, the chief hijra who had willingly answered all his intimate questions, delightedly accused Rupert of flirting with her. Rupert played along: she was a magnificent figure who brooked no argument.

It was very different in Bombay’s red-light district. Though filming in such places is never easy, we found ourselves talking to a couple of meek working girls (real ones this time). One of them mentioned a baby and suddenly pulled a small polystyrene box from under the working bed, opening it to reveal her one month-old boy – destined to join his sibling at an orphanage. Such scenes are not easy to forget.

Travelling with Rupert and film crew on an overnight train to Goa was an altogether more upbeat experience. Rupert loves train journeys. Faced with the long corridor of bunk-bed curtains in the second-class carriage (better for filming than first-class, and Rupert was surprisingly unfussed by such privations), he delighted in imitating that scene in Some Like It Hot when Marilyn Monroe – or is it Tony Curtis? – invites friends to her bunk. We got some strange looks from fellow passengers . . .

Our trip to Goa was prompted by a Burton story of visiting a convent there and falling in love with a nun. Rupert bonded so well with the present-day Mother Superior that she needed no persuasion to join him in a delightfully tuneless rendition of How Do You Solve a Problem Like Maria? I’m not sure the nuns understood what we were doing there, but they welcomed us with enthusiasm – and were truly charmed that Rupert, brought up a good Roman Catholic, wore a rosary (made, as he pointed out to them, from a particularly fine set of black pearls).

Burton was a maverick who firmly turned his back on Victorian convention. Rumours about his own sexuality were rife. In an appendix to The Arabian Nights he conceived a bizarre theory concerning a geographical band across the world – calling it the Sotadic Zone – in which homosexuality was both common and accepted. Thus we found ourselves filming a masseur in Cairo who offered his male clients extra services. Filming this scene late at night – negotiations had been lengthy – the masseur eventually agreed to be interviewed so long as we didn’t show his face. Rupert’s conversation with him, while being gently massaged, leaves very little to the imagination.

Beyond sex, Burton was fascinated by religious ritual. A phenomenal linguist and a consummate actor, his most extraordinary feat was to go on the haj, the sacred annual pilgrimage to Mecca. He was determined to present himself not as a convert but as an authentic Muslim, born and bred. An incredibly dangerous thing to do – discovery would have led to instant death – his success demonstrates his remarkable skill at deception and disguise, his courage and what an anthropologist Burton fan whom we met in Cairo called his “moral flexibility”. Rupert spent the night in the Sahara to get a feeling of Burton’s Arabian odyssey, though we did not even consider replicating his most daring feat.

It is at Burton’s tomb in a cemetery in Mortlake, southwest London – a bizarre and voluminous Arab tent in stone – that Rupert concludes the film, peering through a clear glass window at the great man’s resting place below. How weird to be able to see the actual coffin of a man who died in 1890. But everything about Burton was unconventional, and I hope that Rupert’s pursuit of his legend is appropriately idiosyncratic and uninhibited.

Victorian Sex Explorer, Mon 9 Jun 2008, C4, 9pm

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