The depreciative noun chumocracy is composed of:
– the informal noun chum, designating a close friend;
– the suffix ‑ocracy, forming nouns designating forms of government or groups who exercise political or social power.

The noun chumocracy designates a culture characterised or dominated by influential networks of close friends. In British Politics, this noun has come to specifically designate:
– government, or the exercise of power, characterised by the appointment of friends and associates to positions of authority, without proper regard to their qualifications or to due process;
– a dominant or ruling class consisting of an elite or powerful group of people with interconnected friendships and backgrounds.

The noun chumocracy has been particularly used, in reference to the COVID-19 pandemic, of Boris Johnson’s ¹ government—as illustrated by the following from U.K. secretary resigns over kiss, by the Associated Press, published in the Los Angeles Times (Los Angeles, California, USA) of Sunday 27^th June 2021 [page A4, columns 3 & 5]:

LONDON—U.K. Health Secretary Matt Hancock, who has led the country’s response to the COVID-19 pandemic, resigned Saturday, a day after apologizing for breaching social distancing rules with an aide [i.e., Gina Coladangelo] with whom he was allegedly having an affair.
[…]
The government is […] facing questions about the circumstances under which Hancock hired Coladangelo, a university friend who joined the Department of Health last year. She was initially employed as an unpaid advisor and this year became a non-executive director at the department, a role that pays about $21,000 a year.
Johnson’s Conservative government has been branded a “chumocracy” by critics for hiring special advisors and contractors from outside the civil service without long-customary levels of scrutiny.
Hancock’s department has been accused of waiving procurement rules to award lucrative contracts for protective equipment and other medical essentials, often to personal contacts.

¹ The Conservative politician Boris Johnson (born 1964) served as Prime Minister of the United Kingdom from 2019 to 2022.

The earliest occurrences of the noun chumocracy that I have found are as follows, in chronological order:

1-: From the column The Man About Town, by William P. Frank, published in the Journal-Every Evening (Wilmington, Delaware, USA) of Tuesday 22^nd June 1937 [page 9, column 1]—this is an early, isolated, and humorous use of the noun chumocracy, occurring alongside the nouns chumship and chumtopia:

Chumming Along

If three certain gay young men have their way, the world is soon to hear of the great order of Chumship.
It is still in the embryonic stage, this fellowship order—and in the punning state, at that.
But it has possibilities.
Chumship is the order of noble friends. They aim for Chumtopia and their “national” anthem is “Chump, Chump, the Chums Are Chumming.”
They wish to establish Chumocracy through the breadth and length of the land.
And their watchword is:
“Wilt be my chum this year?”
All these three noble chums need is a publicity man and a financial wizard. Maybe they could charge 50 cents membership—and then watch out.
Chumocracy marches on!

2-: From the following television review, published in The Sunday Telegraph Review (London, England) of Sunday 22^nd September 1991 [page XXV, column 7]:

Next Stop Hollywood: Ray’s Male Heterosexual Dance Hall
C4: 10.00–10.30 pm
A promising start for an anthology of short films by new American directors. Presenter David Puttnam explains that all were made, as part of an “innovative discovery program”, during his time as head of Columbia Pictures. Bryan Gordon’s appropriate opening movie is a metaphor for the chumocracy which determines success and failure in workplace competition. The hero doesn’t know where to look for the right chums until he is directed to Ray’s dance hall. Here he must distinguish between the wimps and the “powerful people” and let it be seen that he is dancing with the right men.

3-: From The Guardian (London and Manchester, England) of Monday 10^th August 1992 [page 20, column 1]:

A cosy cabinet of complacent chums

IN MARGARET Thatcher’s ² day we didn’t really have Cabinet government. Now her reign of terror is over, […] all is entirely changed, you’ll be happy to hear, under nice John Major ³. […] He even sums up at the end of the meeting rather than, as she used to do, at the beginning. He is open to all opinions. He lets the discussion flow. All agree that he’s perfectly splendid. Except for one thing: even now their dominatrix has gone, great issues of national policy are still not fully debated. They are all so agreed about everything, it seems, that debate is pointless. […]
“The Cabinet is a much chummier place now” says Kenneth Baker, himself now excluded from chumhood, “It’s a bit like the Chum’s Own Paper.” […]
Is this not strange? The world outside is in turmoil. […] Even loyal back benchers don’t like what they are seeing in their constituencies. Yet still the chums are untroubled.
There may be some excuse for the older hands. The Thatcher years must have left them traumatised. People long imprisoned under such regimes sometimes find that when freedom comes they don’t quite know what to do with it. But what of the newer and younger members who escaped such subjection? Are they simply too thrilled by finding themselves admitted to the chumocracy to be troubled by vulgar doubt?

² The Conservative politician Margaret Thatcher (1925-2013) served as Prime Minister of the United Kingdom from 1979 to 1990.
³ The Conservative politician John Major (born 1943) served as Prime Minister of the United Kingdom from 1990 to 1997.

4-: From the following television review, published in The Sunday Telegraph Review (London, England) of Sunday 6^th September 1992 [page XXIV, column 3]:

ANDREW DAVIES has written an entertaining sequel to his hit comedy series A Very Peculiar Practice to open the autumn strand of Screen One film fictions.
Honourable and naïve Dr Stephen Daker (Peter Davison), his enigmatic wife Grete (Joanna Kanska) and manic buffoon Dr Bob Buzard (David Troughton) are reunited to face the manifold hazards of A Very Polish Practice (BBC1: 9.25–11.00 pm).
They discover that a vividly unruly nation, in transit from communism to capitalism, is a “chumocracy” bound by a single rule. It’s not what you say or do, it’s who you know, that counts.