While politicians tramp round the country, vying for our attention and eating food in embarrassing ways, it’s easy to forget the silent procession of government. The people who usually run the country aren’t there, yet the country runs. Who is in charge?

Practically speaking, for the next six weeks the country is in the hands of a twenty-five strong club of advisers: the Permanent Secretaries. Here’s a challenge for you. Name one.

Considering what they do, the top tier of Whitehall is a remarkably obscure cast. Other than a brief music hall vogue in the late 1940s that culminated in "Dear Mr Prohack" — a baffling film about a senior Treasury official completely lost in the world outside Whitehall — the Permanent Secretary in popular culture pretty much begins and ends with Sir Humphrey Appleby, Yes Minister’s dexterous smoothie.

This is odd. These people run the country’s largest workforces. Most are responsible for wisely spending billions of our pounds. They are, in Max Weber’s famous phrase, the "permanent residents in the house of power". Yet who they are, what makes them tick, and why they take on their weighty roles, is largely unexplored territory.

The Permanent Secretaries club usually meets once a week, on Cabinet day. This gathering is called "Wednesday Morning Colleagues". At these hour-long meetings, ministerial gossip and not-quite-amusing banter about absent peers is exchanged. Inter-departmental arguments are resolved in the margins. There might be a presentation from a team that is currently flavour of the month with the Cabinet Secretary, which is politely ignored by most of his colleagues.

They ignore it because the civil service — like most British institutions — is unified in name only. As with Oxford or Cambridge universities, where the city provides the brand and the individual colleges have the power, the Civil Service is a gossamer wrapper lightly draped around departments. Permanent Secretaries each control their own fiefdom, and largely leave each other alone.

"Wednesday Morning Colleagues" sounds more like a Christian fellowship coffee morning than a gathering of the country’s most powerful advisers. This is quite deliberate. Whitehall avoids terminology with trappings; it makes the bureaucracy vulnerable to accusations of having ideas above their station. The role "Cabinet Secretary" could barely sound any more functionary; one might think he hands out the tea. The Cabinet Secretary is the most powerful official in the land. He does not hand out the tea. Officials know the power of words, and the words of power.

If you ever get the chance to meet one of these unusual characters, be prepared for an anticlimax. Modern-era Permanent Secretaries tend to operate in camouflage. Not for them the tycoon’s sharpness, media magnate’s bombast, or senior politician’s gloss. If you’re on fine form, you may get the privilege of watching them move from first through to second or third in their intellectual gearbox — you’ll notice when they do — but don’t count on it. The very best will leave an impression that fades from your memory almost as quickly as you acquire it; footprints near the sea.

The job of most Permanent Secretaries is to head up a ministry of state and play chief adviser to the politicians responsible. (Some have other roles; the chief scientist, chief statistician and a couple of national security jobs.) Most have spent their entire careers working in the backrooms of government to reach this point. For the majority, being Permanent Secretary is both the peak and the last big job of their career; a portfolio of board memberships, Oxbridge college pastures and the lecture circuit awaits after they move on.

While Permanent Secretary may be their last job, they generally have a few goes at it. Six of the current crop are on at least their second department. Spending just three or four years in post before moving on is typical. Their brief tenure means that junior officials find themselves exchanging bosses like Panini stickers ("Got. Got. Got. I’ll swap that Romeo shiny for Devereux, Putnam and all my Manzonis.") Permanent Secretaries do not reach the top because they know the most about health, or defence, or tax. They are there because they know most about being a Permanent Secretary.

To the uninitiated, this seems odd. How does this make them qualified to advise their ministers? And having scaled the heights, what do they actually do when they get there? Sir Robert Devereux, the Department for Work and Pensions’ top official, recently told MPs that a Permanent Secretary needs to be able to build good relationships with ministers, understand policy, and be capable of leading large organisations. But what does that actually mean?

In reality, today’s Permanent Secretary needs to be master of three things. She will be a formidable player of the four-dimensional chess that is Whitehall’s office politics. She will be able to read between the lines of officalese to uncover the unexploded political bombs that lie within a myriad of papers and reports. Finally, she will be trusted by her minister to dive on those bombs before they get too close. There are other elements to the job of course — rallying the staff, for example — but are seen only as a bonus.

To seek a Permanent Secretary position, you must have an interesting personal relationship with power. Most civil servants shrink from the word, prefering to express their ambitions in terms of "influence". This is mostly pettifogging. Of course senior civil servants seek power. However, being wordsmiths, they are painfully aware of how such yearnings could be interpreted as shadowy puppet-mastery. Permanent Secretaries don’t really want that. Their desire for power usually takes a very specific form — it must be private and self-denying.

This dynamic contributes to the civil service’s enduring peculiarities. Here you have a set of leaders whose instincts all point to, quite literally, leading from the back. This suits minister’s egos, allows top officials time to manage the constantly delicate office politics, and keeps them out of the media eye-line. Such behaviour has reached the status of constitutional norm, insofar as that really means anything in this country. But it inevitably makes Whitehall’s own management culture of secondary importance, strange and dysfunctional.

Permanent Secretaries have behaved in this way for so long it is easy to forget they were once more at ease with leading from the front. It’s easy to dismiss Whitehall’s great reformers as products of a long-gone Victorian age; people like Sir James Kay-Shuttleworth, a pioneer of public health, or Sir Robert Morant, who pushed the expansion of secondary education. But Britain had formidable post-war advisors with strong views who weren’t afraid to hide them. There aren’t many now.

There is an argument that says Permanent Secretaries and those who aspire to the job must be obscure characters in order to properly serve. That is probably true of their job as it’s currently conceived, and coincides nicely with the British fetishisation of secrecy still prevalent in certain circles. The question is whether that is what Permanent Secretaries really ought to be doing. With post-Brexit politics obviously too complicated for a small group of flapping ministers to handle, it is a shame the Permanent Secretaries have felt unable to step up. Perhaps the risk of emerging from a politician’s shadow is greater when the shadows cast by ministers are shorter than they once were.

In decades gone by, the place to find Permanent Secretaries was Brooks’s, the gentleman’s club on St James’ Street. These days, it’s Twitter. Most of them are on there somewhere, encouraged by Sir Jeremy Heywood, the current Cabinet Secretary. To his credit, Heywood freely concedes that his is “the most boring Twitter feed in modern Britain” but views this “as a badge of honour". Having worked out that complete absence from social media would represent an unusual position more worthy of comment, Permanent Secretaries have identified an even quieter response. Take part, but do so in the driest way possible. Quite inspired, really. The only official not to get the memo is ex-head of the Treasury, Sir Nick Macpherson, who in comparison with Sir Jeremy tweets like a drunk trawler captain on high seas.

Staying cloaked even in plain sight is an entirely rational response for any serving Permanent Secretary — not many people enjoy being on the front page of the tabloids — but not an especially courageous one. The Permanent Secretary’s club may need to take long, hard look at whether well-intentioned passivity is in the national interest for what is to come.

Like most public servants, the true quality of a Permanent Secretary comes down to how much curiosity they show in the people they are charged with ultimately serving. Bad police officers look the other way from the drug deal. Bad nurses look the other way from the dirty ward. Bad permanent secretaries look the other way from the collision of government policy with reality, and watch the slow-motion train crash play out. Truth to power is spoken only in whispers.

Some of the current cohort have made looking the other way an art form during recent project failures. When they hand back the reins of power back on 9 June, the Permanent Secretaries will have a choice to make.

Andrew Greenway is a former senior civil servant who has worked for five UK government departments. He writes regularly on Whitehall and tweets at @ad_greenway.​