The BBC has rightly been criticised for its weak referendum coverage. If the broadcaster had done a better job of challenging interviewees, informing the public and making room for a variety of viewpoints, voters would have had a better chance of sifting fact from fiction. The BBC, after all, dominates our news coverage: 77% of the public use it as a news source, according to Ofcom.

The most common criticism aired against the BBC is one of phoney balance – namely that it gave equal airtime to experts and their opponents’ unsubstantiated bluster. But this is probably not the most serious charge. After all, it would not have been fair to deny the two sides of the referendum equal airtime or to keep off the air campaigners who were telling fibs or spinning fantasy.

However, what the BBC could and should have done was grill its guests more vigorously – and make more space for coverage that didn’t fit into the tired Punch-and-Judy style battle between spokespeople put up by the two official campaigns.

James Harding, the BBC’s director of news, gave a defence of its referendum coverage in The Observer last week, writing: “We have to deliver ‘due impartiality’ and ‘broad balance’, terms designed to ensure that we are free to make judgments on the validity of stories, that we challenge facts and figures, that we acknowledge that different people speak with different levels of authority on a subject.”

Harding backed up this argument with four examples of how the BBC had challenged the “squeakier claims” made by politicians. There were, indeed, some cases in its thousands of hours of coverage when journalists grilled their interviewees effectively. And there were some broadcasters who really made their guests squirm. Andrew Neil stands out, in my mind, as the most effective interviewer.

Not enough grilling

But there were many times when the BBC didn’t challenge its guests adequately. I paid special attention to its agenda-setting Today Programme in the early period of the campaign – when the terms of the debate were largely set – and noted many such cases.

For example, it let Andrea Leadsom say falsely that we send £350 million a week to the European Union on March 8 and Gisela Stuart say the same on April 15. During that interview, the Vote Leve chair also promised to use the money for the NHS – a disgracefully false promise. As late as May 11, The Today Programme allowed Boris Johnson to say we are sending the EU £20 billion a year.

Other failures included letting interviewees spread the myth that the EU needs us more than we need them. Chris Grayling said this on March 10, without being adequately challenged, as did John Redwood on March 22 – though, to be fair, he was quizzed on this when he returned to the airwaves on April 18.

David Davis was allowed on March 24 to get away with saying we can’t stop killers with EU passports coming to the UK. We can. And Leadsom wasn’t challenged sufficiently, in her interview on March 8, when she said 60% of our laws are made in Brussels.

I wish I could play these interviews again and share them with readers. But they are no longer available on the BBC’s website. When I asked for clips, a spokesperson wrote back: “Unfortunately the website is the only public source.”

I am not sure why The Today Programme didn’t rise to the occasion. Maybe its presenters and researchers were not on top of the subject matter in those early weeks. They certainly sometimes appeared ill-prepared for so important and complicated a subject, although to be fair they did seem more top of some of the arguments such as the lie about sending “Brussels” £350 million a week as the campaign wore on.

Maybe they were taken aback by the sheer ballsiness of some of the Leave camp’s claims. When Johnson came on air, he flattened John Humphrys like a Challenger tank, telling the presenter at the end he could “take back control of the interview”.

Maybe the BBC’s referendum guidelines are also to blame. The word “challenge” doesn’t appear anywhere in the long document.

Punch and Judy shows

This wasn’t the BBC’s only failing. It also allowed too much of its coverage to become a Punch-and-Judy style battle between the official campaigns. The broadcaster, of course, had to give a lot of airtime to Vote Leave and Stronger In. But it allowed its coverage to be virtually dictated by their agendas.

I know the Remain side of the story better. Stronger In had a “grid”, on which it set out what stories it wanted to push on particular days and which people it wanted to push those messages. It coordinated this grid closely with Craig Oliver, David Cameron’s director of communications. Indeed, Stronger In was effectively in Number 10’s pocket. It rarely put forward people who weren’t on message with its Project Fear strategy.

The BBC should not have allowed itself to be manipulated in this way, particularly since it was aware of the potential problem. Its guidelines said: “Where there is a range of views or perspectives, that should be reflected appropriately during the campaign.” They went on to say: “The designated Campaign Groups – whilst offering spokespeople to programme-makers and other content producers – cannot dictate who should or who should not appear on BBC output.”

But the broadcaster didn’t do enough to resist the pressure. As a result, Downing Street and its puppets dominated the Remain camp’s share of airtime, and people who wanted to make a positive case for Britain’s involvement were edged out. Even Gordon Brown – who was trying to argue that we should lead Europe, not leave Europe – found it hard to be heard.

Another consequence was that the BBC didn’t do enough to advance its mission which is “to enrich people’s lives with programmes and services that inform, educate and entertain”. One way to inform would have been to rely less on shrill, highly scripted voices from the campaigns and encourage contributions from more nuanced voices. This would have done more justice to the complexity of the issues. But experts such as Charles Grant, founder of the Centre for European Reform, arguably Britain’s preeminent European think-tank, and Lionel Barber, the Financial Times editor, struggled to get on the airwaves.

For every such example, the BBC could presumably come up with a counter-example. But when its senior figures search their souls, do they really think they fulfilled their mission of informing and educating the public well during the referendum? And, if not, what are they going to do about it? How about an independent, public audit of how the BBC fared during the referendum backed up by recommendations on how to do better in future?

The world is not getting any simpler. Hard, honest thinking about how to cover often very complicated questions could stand the BBC in good stead. Audiences and license fee payers definitely deserve it.

Hugo Dixon is co-founder of CommonGround as well as editor-in-chief of InFacts. You can sign up as a supporter here.