It is 1966. The Beatles' Revolver has just been released, and the most popular group in the world have been introducing their listeners to, among other things, the effects of LSD. Specifically, in the song She Said, She Said and, most unambiguously, in the sonic dreamscape of Tomorrow Never Knows. Nothing like it has ever been heard before in the popular arena. Unless you count the unearthly music created by the BBC's Radiophonic Workshop for their new, hugely successful show, Doctor Who.

But there have been problems with that show: its star, William Hartnell, is in poor health, and relations with the new production team are not at their best. The show must go on, but the lead actor has to be replaced. At around the same time John Lennon is turning his blown mind into permanent song, an idea of simple genius is hit upon: the doctor can regenerate, which in practical terms means that any actor of sufficient charisma and talent can take on the role. But for the audience to assent to this, it has to be taken seriously, the implications of what such a change might mean to a creature such as the doctor taken on board.

An internal memo describing the transformative process – now made available on the BBC archive website – puts it like this: "The metaphysical change which takes place over 500 or so years is a horrifying experience – an experience in which he relives some of the most unendurable moments of his long life, including the galactic war. It is as if he has had the LSD drug and instead of experiencing the kicks, he has the hell and dank horror which can be its effect."

Although the memo has all the hallmarks of having been written in haste – never mind the repetition of "experience"/"experiencing", the previous paragraph, equally brief, uses the words "horror" or "horrifying" three times in two lines – it seems as if the author of the memo knows whereof he speaks. If he has not had a bad trip, he knows or has read about someone who has had one. Or has certainly been following the sensationalist literature on the subject.

But transformation was certainly in the air – or on the air, in the case of Hartnell's metamorphosis into Patrick Troughton. Is it any accident, I wonder, that LSD had, vicariously or not, such a regenerative effect on the two most popular British cultural phenomena of the time, to the extent that people are still listening to the Beatles today, and millions are still going to be tuning into Doctor Who next Saturday?

It is tempting to think that it is the case. Doctor Who always was pretty trippy – it's not just that the mise-en-scène generously allows for a certain expansion of the mind at the point of creation, but at the point of reception, too. Many a student, I suspect, during one of those breaks from their studies that they very occasionally allow themselves, has relaxed to an old Doctor Who video or DVD while under the influence of psychotropic drugs (I freely admit that I have, and can still recall, from the fringes of my consciousness, someone asking where I was, and hearing the reply, "he's on Planet Zog", which at the time I found rather funny).

As to whether any of the show's writers or creators dreamed up any of its zanier flights of fancy while under the influence of anything stronger or more illegal than you could get in the Television Centre canteen, that would be to traduce the powers of the imagination, and unless the BBC archives available to us become even more frank than they are already, must remain a matter of speculation; but drugs must have had something to do with the change that turned the Britain of the 1950s – the most boring country on earth, as David Hare described it in his memoirs – into the Britain of the 1960s: one of the most interesting, if not the most.

This is not to minimise the dangers of using hallucinogens as a means of producing or appreciating art (the stoned do appreciate a lot of rubbish). To take the most visible example among countless invisible ones, Syd Barrett wouldn't have destroyed himself without LSD – but then we wouldn't have The Piper at the Gates of Dawn either. No great loss, you say?

Listen to it again. It's the best thing Pink Floyd ever did, in not only my humble opinion. But when it comes to composing high art or literature the effects of the pharmacopoeia are, almost without exception, pernicious. Hunter S Thompson could get away with it; and his example inspired no one to anything good that I can recall.

But when it comes to producing popular culture, a dash of the psychedelic can be truly inspirational, and something in our readiness to be amazed connects to this, whether we're under the influence or not. You don't have to partake of the drugs in order to enjoy their effects second hand, as millions of clear-headed Doctor Who (or indeed Beatles) fans can attest. This week's episode, I gather, involves Winston Churchill hiring Daleks to fight the Nazi menace, and Spitfires in space. I'm not saying anyone was off their head when they came up with that idea. But now that memo is in the public arena, I can't help thinking that they should have been.