The great countercultural movement that we all know from the mid-1960s was epitomised by popular music. But within a few years another shift happened: the birth of alternative theatre.

I doubt if anyone would have been prescient enough to see it coming. Look at the theatre scene prior to that. The West End was deeply conservative. There were a number of interesting plays at the Royal Court – Willis Hall's The Long and the Short and the Tall; Arnold Wesker's Chips with Everything –but they were created by a predominantly older generation, one influenced by their experiences in the armed forces and conflicts such as the Malayan war. Although radical in voice they were still rather formal plays. The only obvious contender for alternative theatre was Joan Littlewood at Stratford East.

The removal of the Lord Chamberlain's office of censorship in 1968 had a liberating effect – albeit a drip-drip one rather than something that happened overnight. And when Jennie Lee, Nye Bevan's wife, took over as minister for the arts she obtained a completely new financial settlement. The Arts Council, which was quite a radical body at the time, started investing in small-scale theatre. But as much as anything it was the growth of the new universities that created the seedbed that allowed alternative theatre to happen.

There was a can-do attitude about the new theatrical scene. People didn't have much money to spend on their productions – certainly the touring companies didn't. Virtually all their money went into maintaining a van that could stay on the road long enough to fulfil their performance obligations.

We were inspired by Brecht and Peter Brook, by the notion of a spare theatre that did away with gloss and the proscenium arch, and instead created something that could be put on in genuinely public spaces rather than formal theatres. The nakedness of the décor was partly a political statement and partly born out of necessity.

By the early 1970s I was in my mid-20s. Virtually all my conscious life I had been involved in theatre – I had been a child actor – but as a young man who had experienced the 1960s, British theatre seemed remote from my aspirations in life – theatre was still a posh thing, a middle-class thing, something for an elite.

It was the new groups that were impressive rather than individual plays, few of which I can readily remember. What was exciting were the statements behind the plays. Red Ladder's set itself was a political statement – "We are red and we are going to use a ladder and nothing else, and that's it". I found that very exciting. And then I saw Monstrous Regiment and the Women's Theatre Group. The idea that there would be theatre companies solely described by their gender was remarkable.

I remember first realising that there were all these other groups and recognising how similar we all were. To me it was a rather miraculous thing that me and my mates had decided we wanted to do something different and – within a year – we discovered countless other groups of young performers had come to the same conclusion.

Another radical movement occurred at the end of the 70s, of course, albeit radical in a very different way: Thatcherism. The very encouraging context in which we had operated in the early 70s all but disappeared by the early 80s – and so did a lot of the funding. It wasn't just that the work got absorbed into the mainstream. As the actors got older, that gruelling lifestyle became less attractive and they had responsibilities and families and so on. Soon the directors we had worked with were attracted to the larger companies, but they still wanted to work with people who had gone through the same alternative experiences as they had.

In my own company, Avon Touring, there were a number of directors who went on to work at the RSC, the National and the Donmar – and they took many of us actors with them. I think we felt able to work in those big, national companies without any sense of betraying our aesthetic ideals, but there was no doubt that the smaller companies began to disappear and the larger, better funded companies took over that work.

You may have noticed that alternative theatre didn't actually bring down capitalism. In many ways, what you might call constitutional politics – the politics of Westminster and the judiciary – remain to this day remarkably similar to how they were in the 1950s. But what has changed is our nation's cultural politics. And I think alternative theatre had an influence far beyond its size in helping to change attitudes towards for instance gender, sexuality and, to quite a large extent, disability. The founding of Graeae by disabled actors was a huge political statement that you forgot at your peril. The culture of theatre itself changed. It was so hierarchical and pyramidical prior to the explosion of alternative theatre, and it was never the same afterwards. And it had an enormous influence way beyond what you might initially imagine.

I have always felt that the rise of what became known as alternative comedy was born out of the loins of the alternative theatre movement. And out of both of these phenomena so much of British performance art has arisen. Although whether it could be called "alternative" now is up for debate – we live in such a fractured society now. When alternative theatre started, there seemed to be a kind of status quo in all fields which was pretty easy to attack and critique wherever you were in the country and whatever audience you were playing to. But nowadays audiences – and their experiences – are much more fragmented. The idea of a dissident theatre is much harder to define. But I do have a dream that if things get much more difficult for the majority of people in this country then a new alternative cultural movement will arise to express that anger. But who is to say that next time round it will be through theatre, rather than some other art form?

What is extraordinary is that such a recent history has been all but forgotten up until now. An awful lot of our activity wasn't recorded. We were all so busy and so transient that much of the documentation got lost along the way.

These were plays, however effective they might have been when they were originally created, that were never going to be bound in leather and put in public libraries. It was all much more ephemeral than that.

• Tony Robinson will open the exhibition Restaging Revolutions: Alternative Theatre In Lambeth and Camden 1968-88 at Camden Archives tonight. The exhibition runs until 10 May 2014