My daily commute takes me past Grenfell Tower. When I first saw the burnt-out building from the train window last Thursday morning, it came as a shock. Even though images of the blaze and its aftermath had filled news bulletins throughout the previous day, seeing the tower block without the filter of a TV screen was utterly gut-wrenching.

Plainly there are questions about the tragedy that require urgent answers – not only about how this disaster could have happened but also about the lackadaisical response from the local council in its aftermath. No wonder those residents who escaped the fire are angry: what they have been through is frankly unimaginable.

In the absence of clear leadership, however, some of that anger has been channelled into conspiracy theories that simply don’t stack up. Walking out of Kensington Olympia station on Friday I heard a woman having a heated conversation on her mobile phone, angry at the failings of politicians to respond effectively to the catastrophe.

What made matters worse, I heard her say, was that the Government was deliberately covering up the Grenfell Tower death toll – known by everyone on the ground, she continued, to be at least 100.

At the time, the number of confirmed deaths was 17, although the police had been clear from the beginning that the death toll was likely to be significantly higher.

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Shortly afterwards, Lily Allen told Channel 4 News that firefighters had told her that close to 150 people had been killed. She went on to say that the death count was being was being “downplayed by the mainstream media”. Ramping up the establishment cover-up theory, The Swawkbox blog then claimed the Government had issued a defence notice (D-notice) to ensure a media blackout.

Quite where the D-notice theory came from is unclear. D-notices – now formally known as DSMA-notices – are a standing set of non-binding requests relating to the media’s coverage of UK military operations, assets and personnel. They exist as part of a voluntary arrangement between the Government and the media, and they are publicly available should anyone wish to consult them. While the committee that oversees the system occasionally issues guidance in relation to one of the five standing D-notices, new ones are not simply issued at the whim of the Government.

If the D-notice theory was demonstrably wrong, it is perhaps easier to understand the broader idea of a conspiracy of silence over the number of fatalities at Grenfell Tower. Early statements from the authorities confirmed six deaths, then 12, then 17 – even though, with dozens of people missing, it was fairly obvious that the final death toll would be much higher.

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Nevertheless, neither the police, nor the Government, nor the media at any stage suggested that those early figures would not be revised upwards. That relevant agencies were seeking to approach the difficult task of accounting for the missing and identifying the dead with due rigour hardly seems to be something that is worthy of criticism. Today, 79 people are confirmed to have died or are presumed dead. The figure may rise again, but this is not the stuff of cover-ups.

Still, the fact that so many people are ready to believe that it is possible for the truth about the Grenfell Tower victims to be kept under wraps should concern us as a society. It shows that faith in government and in key authorities, including the police, has been thoroughly eroded. It demonstrates too that some people are more ready to believe rumours and social media than what is so dismissively referred to as the “MSM”.

Past experience is partly to blame – look at how long it took for the truth to come out about Hillsborough. The present, very real failures of politicians and others either to prevent last week’s tragedy or to respond effectively to it inspire further distrust. In that context, cynicism seems entirely reasonable.

The problem with such extreme cynicism, however, is that it assumes – without due reason – ulterior motives on the part of good people. It also feeds a destructive belief that a shady establishment is deliberately lying to “the people” for its own corrupt ends. And in the end, it can enable real misdeeds to be hidden because anger comes to be directed at imagined monstrosities.