It is 11 years, to the month, since Tony Blair left Downing Street. Yet by his own account, before noon every Wednesday, wherever he is in the world, he still feels an icy chill – an instinctual reaction to the imminence of prime minister’s questions.

On paper, PMQs should not hold such terror. The prime minister needs simply to show up in the House of Commons once a week and answer 40 minutes of questions from MPs, half from their own side and half from the other, including six from the opposition leader. But as this new study makes clear, the event has a significance far greater than its parts.

It has the power to shift the prevailing political mood and the stock of each party leader, being the occasion for an instant collective judgment that hangs in the air of parliament until at least the following week. The fact that it happens so regularly should diminish its importance, but in practice, this only makes the pressure relentless. Harold Macmillan, who in 1961 became the first prime minister to face regular question sessions at fixed times, confessed in his retirement that he felt physically sick preparing for each “ordeal”. This was a man who had fought on the Somme.

I have stood in at PMQs for Jeremy Corbyn on just four occasions, and it hasn’t yet traumatised me as much as it troubled Macmillan or Blair, but nothing can prepare you for the experience. Many people get anxious before speaking in public, but imagine speaking while 300 MPs screech and roar to put you off – shouts that prevent you from hearing yourself speak and which it would be unwise to try to make out.

This book does the best job imaginable of putting you in the shoes of those who have faced that test, and by shining a light on this one aspect of our political life it succeeds in illuminating the whole. Ayesha Hazarika and Tom Hamilton draw on their first-hand experience of working with Ed Miliband and Harriet Harman, as well as on interviews with Blair, David Cameron, William Hague and George Osborne. They are clearly skilled interviewers, getting each subject to reveal much of themselves, from the unrepentant arrogance of Cameron to the brutal introspection of Miliband. And with the level of honesty that Osborne shows here, I was left itching to read his future autobiography.

Osborne regrets misjudging the mood of the house at his first PMQs when he stood in for Cameron against Hilary Benn in 2015: “I made some nice remark about him but it was inappropriate because he’d raised some terrorism incident. And I knew the moment I said it.” Contrast this with Cameron’s outlook: seven years after the event he still doesn’t know what was wrong with telling Angela Eagle to “calm down, dear” during a heated exchange in 2011. “I don’t think it was particularly at Angela Eagle actually,” he mansplains to the authors. “I think I was referring to Ed Balls, but anyway the point is there was no mens rea, it was not sexist in intent, it was the funny line from Michael Winner.”

I enjoyed the Tory voter who wrote to Theresa May praising her PMQs performances but urging her to chastise the MP behind her doing his “office work” – shuffling papers and making notes – rather than listening to the debate. The MP concerned rang the voter to explain that he was the one passing May her answers. But I shivered reading about the attempted ambushes of prime ministers that blew up in the faces of opposition leaders. Hazarika and Hamilton recall Miliband asking Cameron at the last PMQs before the 2015 election if he would rule out raising VAT. Cameron gave the one answer they weren’t prepared for, “Yes”, then challenged Miliband three times to rule out the prospect of a Labour government increasing national insurance contributions. Perhaps because of the pain of the memory, it is one of the few key PMQs moments when the authors do not simply let the transcript tell the tale.

The VAT misfire jars all the more because of the astonishing effort that went into getting Miliband ready for each PMQs. The book reveals that preparations began almost as soon as the last session ended, involved vast numbers of people – and yet still he would go into the chamber every Wednesday asking whether his strategy and lines were right.

If that seems like overkill for the official opposition, what the book exposes about preparations inside government is equally worrying, in terms of the sheer amount of time and energy involved in commissioning briefing across Whitehall, and taking the prime minister through it. The argument, made both by the authors and their interviewees, is that this is an essential part of Downing Street keeping an eye on what each department is up to, and nipping potential problems in the bud – an excellent concept in principle, but one that does not explain, for example, why the Windrush scandal went unaddressed so long.

But just stirring up the argument is a triumph for the authors. Since 1961, PMQs has moved to the centre of our political life, and since its first televisation in 1989 and the more recent use of Facebook and Twitter to distribute key moments, its importance has increased inexorably. It is high time to have debates about whether its format, length, volume and – most vital – the amount of effort our leaders put into it are right for our age and good for our politics. I hope Hazarika and Hamilton have started that debate. Because as Blair tells them: “It was really important without being truly important, if you can see what I mean.” Yes, after reading this invaluable and enthralling book, I certainly can.

• Punch and Judy Politics by Ayesha Hazarika and Tom Hamilton (Biteback, £20). To order a copy for £17, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.