Vytautas Andrius Graičiūnas was a Lithuanian American management theorist who published a classic study Relationship in Organization in 1933. He mathematically proved that a manager should not have more than four to five subordinates. He posited a formula which showed the number of relationships a manager can deal with, for a given number of reporting subordinates. Those relationships include (a) one-to-one, i.e. manager/subordinate (b) cross relationships subordinate/subordinate and (c) group relationships, e.g. manager/subordinate/subordinate. For 5 subordinates, it's 100; for 6, 222; for 7, 490. Don't worry about the numbers, just realise that the more people you have reporting to you, your ability to effectively manage them diminishes exponentially.
Management theory calls this the "span of control" and is used in the military for command and control functions and also in large commercial organisations.
The Prime Minister of the United Kingdom has a cabinet of 25 or 26 (I couldn't quite figure it out exactly). There are duplications in terms of departments, for instance Baroness Chapman is Minister of State (Development) in the Foreign Office, so presumably reports to the Foreign Secretary rather than direct to the Prime Minister. There are still around 20 departments of state.
So the Prime Minister of the day has a bumper number of people formally reporting to him/her.
There's maybe an argument that a more structured way would enable their job to their job better. It can be argued - as it was by ChatGPT in our...chat - that the PM, as primus inter pares, allows greater autonomy to secretaries of state, but this manifests itself as a problem which is that, once a week, the PM has to answer for everything in government publicly in Prime Minster's Questions in the House of Commons. And is expected to know...everything.
There's another problem, which is relevant to the recent months - in fact arguably ever since the current government came to power. In comparable countries, foreign affairs and world diplomacy are carried out by the Head of State, usually President, leaving the PM to focus on domestic affairs - see France (not a great exemplar of effective government at the moment, I accept). This has been a major problem for Keir Starmer, facing significant global instability and an erratic US President.
So it's no surprise that Starmer is floundering. You'd have thought an experienced manager like him, who had a staff of over 7,000 when he was Director of Public Prosecutions, would be able to use that experience, but I imagine that was a better structured organisation and his job had a single, highly focussed mission. Government is different: not just about continuing an existing functionality; it's often about juggling, and deciding between, a set of bad options. Different problems, maybe requiring leaders with different characteristics.