There's no one precise answer to this, as the crew complements of these ships varied over the course of the war. As new technologies like radar became available, new officers and men joined the ships. Equally, things like floatplanes were removed from the ships over the course of the war, reducing the numbers of men present. Ships that were acting as fleet flagships carried more officers, to serve as the admiral's staff. Burt gives a total of 84 officers for Duke of York when she was acting as a squadron flagship, and 104 for her when she was serving as fleet flagship.

Another important note is the importance of the RN's system of 'branches'. Between the ranks of sub-lieutenant and captain, RN officers (with several exceptions) were 'streamed' into a number of branches. These branches offered specialist training for particular roles. Most officers remained in the non-specialist seaman branch. The next most popular was the rather self-explanatory gunnery branch. Other areas where officers could specialise included the torpedo branch, signals, navigation and aviation. The engineering branch had a separate system of promotion. Officers remained entirely within it, and never moved out of it. Other non-executive branches, like the paymaster branch (supply branch from 1944), were similar.

The most important officer aboard a battleship was the captain, who always held the rank of captain. His job was to command the ship. Backing him up was the commander, who, as with the captain, held both the rank and position. The commander's job was to command the crew, enabling the captain to concentrate on things like strategy and tactics (in the USN, the commander was known as the 'executive officer'). The commander also had a small staff to support him, with a Lieutenant Commander (Regulating) to do most of the paperwork, plus a number of petty officers and other NCOs. The captain would have a secretary, a paymaster lieutenant or sub-lieutenant, to help with his paperwork. In action, the captain would be found on the bridge. The commander was in the afterbridge, ready to take over if the captain was killed. He was also responsible for organising damage control efforts.

Below these two officers, the KGVs had two gunnery officers, a torpedo officer, and a navigating officer. These were the heads of their respective departments. The gunnery officers were responsible for the ship's armament. The torpedo branch's duties, by historical accident, included electrical work. As the KGVs had no torpedo armament, this formed the torpedo officer's main duty. The navigating officer was the ships' main navigator, though all officers of the seaman branch had training in it. He was also seen as the most capable officer for manoeuvring the ship. A number of captains from the seamen branch, out of practice with steering their ships, would delegate to their navigating officers or allow them to overrule them if they made a mistake. The navigating officer and torpedo officer would have action stations with the captain on the bridge, while the gunnery officers were in the director control towers (DCTs). The remainder of the main officer contingent was made up of officers from the seaman branch. This would be a mix of lieutenant-commanders, lieutenants and sub-lieutenants, as required by the ship in action. Each main gun turret would have an officer, while there would be three officers in command of the secondary armament. Four officers were in charge of fire control, in addition to the gunnery officers. Several more would control the anti-aircraft armament. When not in action, the ships' complement was typically broken down into a number of divisions, subdivisions of the crew by either where they worked (for seamen) or by speciality, A ship would typically have 14-15 divisions, each with an officer in charge of them. The ship would carry a number of midshipmen, trainee officers. The number of midshipmen varied according to need and availability, and was never fixed. A sub-lieutenant was detailed to look after the midshipmen.

Beyond these, a KGV would have a number of specialist officers. If floatplanes were carried, the ship would have four officers from 700 Squadron of the Fleet Air Arm. Two of these officers would be pilots, two observers (responsible for navigating and spotting). The KGVs had an accountant officer from the paymaster branch, typically a commander. It would also have two-three more paymaster officers, to supervise the cooks and to do other administrative duties. The engineering branch was the largest specialist branch. Typically, it would have two or three senior engineering officers, commanders or lieutenant-commanders, plus up to ten lieutenants. They commanded some 250 men (though in action ~25% of these would not be in the engine room, but would instead form part of the damage-control parties). A KGV might have a telegraphy lieutenant, responsible for the ship's radios and communications. Officers from the RNVR Special Branch were technical specialists, falling outside the usual executive path. Aboard the KGVs, they were typically responsible for the ship's radar, and for its degaussing equipment - though they might also have other specialities like meteorology. Initially, few were carried, but as radar became more prevalent, numbers rose. The ships also had warrant officers, technical experts who did not have command responsibilities. These included two-three commissioned gunners, plus an ordnance officer and gunner, to man the director towers and ordnance supply. The torpedo officer had a torpedo gunner to act as his assistant, as well as a commissioned electrician. Boatswains were in charge of the ship's boats, as well as, to some extent, signalling. A supply warrant officer assisted the officers of the paymaster branch, while the engineering branch might be supplemented by two-four warrant officers. We also cannot forget the officers of the Royal Marines. A KGV had a 350-strong marine complement, under the command of a major (sometimes a captain due to shortages of senior officers, though aboard ship he would always be referred to as a major). He would have three juniors, captains or lieutenants, plus possibly a Marine warrant officer. Ships might also carry a chaplain, who was a commissioned officer, but wore no naval uniform beyond the naval cap.

As far as medical personnel go, these were the domain of the surgeon branch. Typically, battleships would have three surgeons, plus possibly a dental surgeon or two. These would be accompanied by a number of Sick Berth Attendants (SBAs). The SBAs were junior ratings, with a wide range of duties. They might be closer to a nurse or ward orderly, but might also be expected to act more like a modern paramedic. Typically, six SBAs were carried, under the command of a petty officer. More might be carried to perform specialist duties, like operating X-ray machines or to act as dental technicians in support of a dental surgeon. The sick bays on the KGVs were spacious and modern. That of Prince of Wales was described thusly:

Accommodation in the Sick Bay consists of 22 swinging cots, 4 of which are in an isolation ward. There is also provision for the slinging of 8 hammocks. In an emergency there would be sufficient floor space for 12 or more stretcher cases.

The sick bay was intended to provide initial and emergency care, before wounded and sick men could be transferred to a hospital ship for further care and transport to hospitals ashore.

Cooking was mostly the preserve of non-commissioned cooks. Typically, the menu for the ratings would be drawn up by the warrant supply officer. It would then be approved by the paymaster commander. The food from this would be prepared by the ship's cooks, with 30 being typical for a ship of this size. Each of the KGV's 116 messes would select two-three 'cooks of the mess' to pick up the food from the galley at each meal-time. The officers had their own cooks, plus stewards to serve the meals. The captain had two cooks, the wardroom (officer's mess) the same amount. The gunroom (midshipman's mess) and warrant officer's mess had one each.

As far as gunnery goes, you can see my explanation of the RN's gunnery system here. The captain would select a target using the 'captain's sight'. This was then passed to the DCT. There were three officers in the DCT, one spotting the target, one tracking the rate at which the range and bearing changed, and a gunnery officer in overall control. The inputs from these were passed to the Transmitting Station, which was manned by members of the ship's Marine Band, with an officer or commissioned gunner in command. Here, the Admiralty Fire Control Table, an electromechanical computer, would calculate the firing solution, which was then sent to the turrets. I can't find a good listing of the crews of the KGVs turrets, but the triple 16in turrets on the Nelson class had one gunners mate, fifteen gunnery ratings and two other seamen in the turret itself, along with the officer commanding the turret. The cordite handling room had seven gunnery ratings and nine other seamen, while the magazine itself had four gunnery ratings and 21 others. The shell room had 17 other seamen and eight gunnery ratings, with a gunners mate and eight gunnery ratings in the handling room. This totalled 93 men and one officer.

Not to send you someplace else, but the gang over at /r/warshipporn might very well know something as well... just post a picture of a KGV, and ask at the same time!