Answering this question is a massive undertaking, because the RN was a generally very competent service throughout the war. They were world leaders in anti-submarine warfare, amphibious operations, and surface warfare, while being very competitive in terms of carrier aviation. There were flaws, of course, but the lessons from them were digested and disseminated well. I'm just going to focus on three areas - carrier aviation, ASW and intelligence.

By 1945, the RN had constructed an extraordinarily effective machine for hunting submarines and protecting trade. However, this had gotten off to a rocky start. The interwar RN had failed to anticipate how good killing grounds convoys would be following the advent of ASDIC and improved depth charges. Instead, they believed that the applicable lessons from the first Battle of the Atlantic was that convoys, while good for protecting merchants, needed to be accompanied by roaming hunter-killer groups to actually kill submarines. Such groups were deployed during the early days of the war, with two major results. Firstly, it diverted much-needed long-range escorts from the convoys, giving the Germans easy pickings in mid-Atlantic, which the short-range corvettes couldn't cover. Secondly, it put major units, especially carriers, into the line of fire. This resulted in the loss of HMS Courageous, and nearly in the loss of Ark Royal too. However, the lessons were quickly integrated into RN doctrine. Once the Battle of the Atlantic began in earnest following the fall of France, the RN formed escort groups, concentrating expertise in these specialised units. At first, they developed their own tactics, but this led to issues when two groups had to cooperate. As a result, Captain Gilbert Roberts, of the Liverpool Tactical School, synthesised a new set of tactics from the most effective ones utilised by the escort groups. These tactics were beaten into the officers and crew of each escort by effective training schools, at Tobermory and at HMS Philante in Northern Ireland. This gave the RN's escort force a sound basis in ASW tactics at all levels. On this base, new technological assets were added, to create a world-leading ASW force. The ahead-throwing weapons, such as Hedgehog and Squid, worked much better with ASDIC than depth charges. The RN was the first to introduce the escort carrier, starting with HMS Audacity, a converted merchant ship. These covered convoys against air attack and extended the air umbrella into mid-Atlantic. Escort carriers were again integrated well into British tactics. Ultimately, in conjunction with vast production of escorts in American and British shipyards, they were used to re-invent the hunting groups, to good effect.

Beyond escort carriers, the British, despite the reputation of their carriers, got several things right about carrier aviation. The Fleet Air Arm learned from the early attempts at fighter direction by the RAF, and implemented their tactics at sea. Aboard Ark Royal in the North Sea, Lt Cdr Charles Coke (the ship's signals officer) used radar reports from her escorting cruisers to direct his ship's combat air patrol - the first use of radar at sea in such a way. This concept rapidly passed between carrier crews at an unofficial level, but by 1941 it became official doctrine. Over the war, it developed into a sophisticated system where information from multiple outlying ships and the carrier itself was plotted and synthesised to effectively direct the CAP. This centralised system was far better than American attempts, or the almost non-existent Japanese system. The Fleet Air Arm was also the only true all-weather carrier strike force available. The battle of Taranto, and the battle of Cape Matapan both featured successful night attacks by carrier aircraft. During the hunt for Bismarck, aircraft from Victorious and Ark Royal made attacks in both poor weather and in the hours of darkness. The Japanese and Americans made few comparable attacks - though at the Battle of the Philippine Sea, the USN lost nearly 80 aircraft trying to recover them at night (however, part of this was due to the aircraft having been launched at extreme range, and them running low on fuel before landing). A final area where the RN had an advantage in carrier aviation was in damage control, especially in fire suppression. The RN had, in WW1, lost the seaplane carrier Ben-my-Chree to a major fire in her aviation fuel storage. As a result, there was a conscious effort within the RN to reduce the risk of fire aboard as far as possible. The hangars on the Ark Royal and Illustrious class were set up such that, with the lifts up, the hangars were reasonably airtight, preventing major fires forming (as such a fire would rapidly consume all the oxygen in the hangar and burn itself out). This also prevented hangar fires spreading to other parts of the ship. The ships had a highly effective sea-water dousing system, capable of putting out a large hangar fire in under 15 minutes. This system had more redundancy than the American or Japanese equivalents. It used three separate mains, each covering a separate part of the hangar. The Americans had two (port and starboard) mains, and the Japanese only one. Bomb damage could easily destroy these systems, while on the British it would only knock out the main for that section, allowing the remainder of the hangar to be doused. Finally, the RN accepted losses in fuel storage for safety measures. The aviation fuel was stored in cofferdams in sea-water filled chambers. The pressure of the water prevented fuel vapour filled voids forming in the system, greatly reducing the risk of explosion. The water-filled chambers also insulated the fuel tanks against shock damage, and provided a space for damaged tanks to spill into without creating fire hazards. The value of these precautions can be seen by comparing the damage done to RN carriers to that done to others. On the 10th January 1941, HMS Illustrious was hit by four 1100lb bombs, a 2200lb bomb and a 500 lb bomb. This started a major fire amongst parked aircraft in her aft hangar. However, this fire was brought under control, and did not spread to the rest of the ship. At Midway, four Japanese aircraft carriers were hit by between one and four 500lb and 1000lb bombs each. All four would burn uncontrollably, and would be scuttled. At Coral Sea, the USS Lexington was destroyed by avgas explosions from leaking fuel tanks, as would the Japanese Taiho at the Philippine Sea.

The Royal Navy excelled at collecting, interpreting, and disseminating intelligence in a sensible manner. The Naval Intelligence Department expanded massively over the course of the war, from just 24 officers to nearly 300. This obtained information from a broad variety of sources. Interviews and overheard conversations from PoWs gave the RN a sense of morale amongst the U-boat crews, but it also gave insights into the technical capabilities of U-boats. Captured vessels could also give these insights - when U-570 was captured in August 1941, the RN put her through an exhaustive series of tests until her abilities were fully understood. Sunken ships were plundered for all they were worth. British agents purchased the wreck of Graf Spee in Montevideo harbour, as a way to investigate her early radar. Materials recovered from the wreck of U-33 by HMS Gleaner proved greatly helpful to the cryptanalysis of Enigma. Aerial reconnaissance was hugely important to the RN, but was mostly collected by the RAF. RAF photo-reconnaissance observed Taranto harbour before the RN's raid, and provided the RN with warning that Bismarck had sailed from Bergen. Signals intelligence was in many ways the most important. Traffic analysis, noting the frequency and origin of signals, gave excellent warning of likely attacks, as did an understanding of the basic tactical codes used by U-boats. Radio direction finding (HF/DF) was exceptionally useful for finding U-boats, aided by the German doctrine's requirement to send more messages than really necessary. Finally, the RN used decoded messages, aided greatly by Bletchley Park's breaking of the Enigma. This gave the RN a means to route convoys away from U-boats, as well as intelligence on German long-term planning. Once the intelligence was gained, it was passed to the Operational Intelligence Centre for assessment and distribution. The RN was much more careful about disguising the sources of its information than the Germans were. Precise information obtained from Enigma messages was made less precise for dissemination, and the accompanying information always implied that the source was more innocuous than decrypted messages. The Submarine Tracking Room was probably the most important of the subsets of the OIC, with its responsibility for the Battle of the Atlantic. Taking in every available scrap of information on the U-boats, they were able to supply highly detailed intelligence on every aspect of the U-boat war. This was done in a magazine called the Monthly Anti-Submarine Report, delivered to the commander of each escort vessel. Each issue began with a perceptive assessment of the current situation, followed by reports on new technologies and tactics from both sides, and analysis of battles and activities of the previous month.