The Dundee-born thespian makes the revelation in a new BBC Scotland programme, Addicted to Pleasure, to be shown later this month.
The documentary series, presented by Cox, charts the histories of four substances he believes have blighted Scottish culture for centuries: sugar, tobacco, opium and whisky.
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Cox, 66, revealed he was on a theatrical tour of India when he decided "in the spirit of experimentation" to visit an opium den in Mumbai.
His memories of the experience, he recalled, were of feeling "very at one with the world", adding: "I suppose I shouldn't be saying this on television, but it was a rather good feeling".
Cox told The Herald: "It's something I have spoken about privately but never before in such a public way. I believe you have to be honest and admit your humanity. You can't be above it all."
While he only smoked opium once, Cox admitted to further broadening his horizons on the visit.
He said: "I tried other things. In Calcutta I had bhang lassi, a yoghurt drink with poppy seeds at the bottom which has a slightly hallucinogenic effect.
"There were 'bhang bars' that looked like shoe-shine places. You would sit up in sloped chairs and drink this stuff, almost like a latte, but with opium in it."
He added: "I have no regrets, but I do think you have to be responsible. I was never into it when I was younger because I didn't like the idea of it. I was very puritanical. I thought it was a bit of an indulgence on people's parts.
"When I went to India, I was in an environment when I could try it in the right conditions. It was the conditions that were important. It was only there I could try it – so I did."
In the opening episode of the series Cox talks frankly about how another "vice" – sugar – has impacted on his own life.
He was diagnosed with type 2 diabetes in 1998 and reminisces with his two sisters in Dundee about their sweet-toothed childhoods, recalling how, as a youngster, he would buy "tuppenny" bags of broken biscuits on the way to school.
He said: "Our diet in Scotland has been deadly. The idea that we eat fish and chips at 11pm. We are sensible and have our tea at 5pm – but then we should really stop eating."
Cox suggests Scots have become so addicted to sugar that it is almost taken for granted, like water. "It is insidious," he said. "I did an interview with someone who was addicted to soft drinks. That was mind blowing. But it's only the tip of the iceberg because you realise a lot of people are addicted and aren't even aware of it."
He added: "When you think of the Government health campaigns for cigarettes, they clearly say: 'This will kill you'. Well, I'm afraid the same is true of too much sugar."
Tackling the thorny issue of tobacco consumption, he interviews artist and playwright John Byrne, a lifelong smoker who reveals he had his first cigarette at the tender age of seven.
Cox said: "John is an unrepentant smoker and I have begun to respect that notion. I personally hated smoking and couldn't bear the smell on my clothes. I thought it was an ugly thing, it wasn't sexy."
He said that learning about experimental research into using nicotine in treating Alzheimer's and Parkinson's Disease had changed his viewpoint. "A scientist told me: 'Good drug, bad delivery system'," he said.
The series sees Cox test his theory that many of today's vices first took root during the height of Britain's trading empire.
"My view is that we have not recovered from when we moved from an agrarian society to an industrial one," he said. "There is a discrepancy between our bodies and brains.
"It's as if our bodies are in the middle ages and our brains somewhere in the future. The brain is asking the body to do things it's simply not capable of."
l Addicted to Pleasure starts on BBC1 Scotland, November 26 at 9pm.