During the era of agitprop theatre in the 1960s and 70s, when politically committed companies toured the UK, there was usually a rule that the show would not go on if there was a risk of having more people on stage than in the audience. And even with the hallucinogenic substances that were part of the scene at the time, no one would have imagined that a passionately leftwing theatre show would one day play to an audience of one billion and have a budget of £27m to spend.

But, last Friday night and Saturday morning, that is exactly what happened. Among the spectacular achievements of the 2012 London Olympics opening ceremony was that it marked the apotheosis of a dramatic tradition that had previously been marginalised in this country.

This is not just a critic's whimsy: the key creative forces behind the games – the ceremony director, Danny Boyle, and creative overseer, Stephen Daldry – are children of political theatre. This experience has shaped them at least as strongly as the cinematic credits (Daldry's Billy Elliot and The Hours, Boyle's Slumdog Millionaire and 28 Days Later) with which they are now more commonly associated.

Apart from the era of "agitprop" – a word combining "agitation" and "propaganda", derived from Soviet theatre in the 1920s – there have been three key locations in Britain for leftwing drama: the Theatre Royal Stratford East just after the second world war, the Royal Court theatre from the 1950s onwards and television drama between the 60s and the 90s.

Boyle and Daldry both made their theatrical reputations at the Royal Court, where each had a long period on staff as deputy director and artistic director respectively, while Boyle's screen career began in television, with work for ITV, Channel 4 and the BBC drama and film units during their most ideologically engaged periods.

Both men are too young to have been involved in the Theatre Workshop at Stratford East, but several sections of the opening show seemed to me to nod deliberately to the work done by the pioneering Joan Littlewood, whose celebrated productions, such as Oh, What a Lovely War!, used song, dance, pageant and community participation to make political points in an accessible style – and, furthermore, did so just up the road from where the Olympic stadium now stands. Boyle's tableaux of the industrial revolution and the National Health Service – and the moment when the CND badge was suddenly formed on stage – felt strongly Littlewoodesque, honouring an east London heroine in the same way that David Beckham's participation honoured his local origins.

Another intriguing connection is that the peak years of radical theatre were often subsidised by rightwing governments: the purest expression of the "arm's length principle", by which the British state funded culture, chiefly through the Arts Council, without influencing its content.

Given all this, it was always likely that the show would inflame some conservatives, and, sure enough, it did – as revealed in comments by the Tory MP Aidan Burley on Twitter and the rightwing commentator Peter Hitchens in the Mail on Sunday.

But Boyle's approach can be justified by the fact that the 2012 Olympic bid was initiated and successfully executed by Labour governments at both national and London level. More importantly, the ability to choose what to say, free of political influence, is a fundamental British value, and so merited expression in a show that celebrated the nature of the nation. Following a Beijing ceremony that had to say exactly what the country's government wanted it to, the Boyle event pointedly delighted in saying things our rulers might dispute.

And, from a dramatic point of view, one of the evening's many ironies was that the kind of theatre honed at the Theatre Royal Stratford East and the Royal Court in Sloane Square played to a combined global audience surely greater than all the combined theatre-goers they have ever served.