Royal Air Force
The RAF is steeped in tradition dating back to the formation of the service in 1918, traditions which are alive today. The Squadron is the principle operational unit of the RAF since the formation of the RFC in 1912. Squadron numbers were allocated when the squadron was raised and, along with the badge, became a source of intense pride and distinction.
Currently there are over seventy operational squadrons each with a specific purpose. These include a large proportion of administrative units, scientific units, training units and auxiliary units as well as regular operational aircraft units. Some Squadrons have retained the original type displayed in parenthesis, i.e. No. 1 (Fighter) Squadron, with some retaining the Roman numeral style, for example No. IX (Bomber) Squadron. Other units have retained the origin of its launch, i.e. No. 42 (Torpedo Bomber) Squadron.
RAF Squadrons numbered from 1 to 699 with allocations having many anomalies over the course of history. To gain a full list of RAF Squadrons Wikipedia have concise lists available as well as a multitude of other websites.
The first 150 numbered squadrons were taken by the RFC with the first three being the original 1912 squadrons. The RNAS used the same numbering system after the wings were discontinued in 1917. When the two merged the RFC retained their squadron numbers and RNAS squadrons were given a prefix of 2, therefore the numbers 201 to 299 were allocated to ex-RNAS squadrons, although not all were allocated to the RNAS during WW1, while other 200 series squadrons were amalgamations of RNAS catapult Flights. Squadron numbers 277 to 299 were formed just before WW2 as maritime squadrons in one form or another. A large number of these units were disbanded after WW1 and reformed just before or during WW2.
Numbers 300 to 352 were designated RAF foreign Nation squadrons during WW2 with 353 to 361 being regular RAF squadrons. The numbers 362 to 399 were never utilised. Foreign Nations squadrons were staffed by personnel from countries in occupied Europe under RAF command and control. Polish, French, Dutch, Norwegian, Greek, Belgian, Yugoslav and Czech pilots and personnel formed these units. Between 1940 and 1942 three squadrons were staffed by US volunteers and named ‘Eagle Squadrons’, Nos. 71, 121 and 133 Squadron. When the USAAF arrived in the UK these squadrons converted to American Fighter Squadrons but retained the Spitfires. The Air Forces of Australia, Canada and New Zealand were allotted squadron Nos. 400 to 490. These were squadrons formed under the Article XV Act whereby Dominion pilots and aircrews were trained in the Commonwealth Air Training Plan and sent to any theatre of the war as required. The majority were Canadian squadrons, Nos. 400-443 RCAF (444 to 449 unused). Australian units were Nos. 450 to 467 RAAF although 465 and 468 to 484 were not used. New Zealand were Nos. 485 to 490 RNZAF. South Africa took no part in the scheme.
Nos. 500 to 505 were special reserve squadrons four of which are currently active in the Royal Auxiliary Air Force (RAuxAF). Nos. 510 to 550 were regular RAF units comprising all sorts of operational scope including 10 Turbinlite nightfighter squadrons (Nos. 530 to 539) formed from Turbinlite flights, usually AI Radar equipped Boston Mk.III or Havoc, which illuminated targets with powerful spotlights for the night fighter Hurricane Mk.IIs to intercept. These were possibly the shortest run squadrons of the RAF being formed in September 1942 and disbanded in January 1943. Nos. 567 to 599 were assigned for regular RAF units although only 13 of these numbers were ever used.
Royal Auxiliary Air Force Squadrons were Nos. 600 to 616. No squadron number was allocated to RAF Training squadrons until much later. However, Nos. 550 to 565 were Operational Training Units assigned to Operation Saracen in early 1940 to provide back up in the event of a German invasion.
Nos. 617 to 650 were assigned as regular RAF units although only 19 of these were formed. Nos. 651 to 666 were AOP Squadrons (Air Observation Post) manned by the Army. Some of these units went on to become Army Air Corps squadrons after the war.
Most Universities in the UK have a University Air Squadron with Air Experience Flights attached under the command of No. 6 Flying Training School RAF.
Then there are the Independent Flights unattached to Squadrons. There are currently three operational , Nos. 1310 (Transport using Chinooks), 1312 and 1435 both of which are deployed as Falkland Islands garrison at RAF Mount Pleasant. The Battle of Britain Memorial Flight is maintained at RAF Coningsby with currently 12 operational aircraft for display purposes. So, you could say that the Lancaster, Spitfire and Hurricane were never fully retired.
The most famous unnumbered Squadron is of course The Red Arrows, official name The Royal Air Force Aerobatic Team, which has its own badge and independant identity since 1964 when all display teams were amalgamated to form one. Previous RAF Display Teams were formed from existing squadron units, for example No.92 Squadron ‘Blue Diamonds’, and used a multitude of aircraft over the years. The Red Arrows use the Hawker Hawk I/II many of which are allocated in rotation from training units. Pilots are RAF with at least 1,500 hrs flying time on a three year posting.
Fleet Air Arm
Originally in 1924 the FAA used numbers 401 to 499 for spotter flights on Royal Navy battleships and cruisers. In 1933 the flights were amalgamated into squadrons using the allocated 700 and 800 range. After the Admiralty regained control of the Fleet Air Arm in 1939 all FAA Squadrons retained numbers 700 to 899. Once allocated the numbers were reused for regular squadrons as well as reserve squadrons with a prefix of ‘1’. The FAA currently have 15 operational Naval Air Squadrons including 809 NAS which operates the new F-35B.
The FAA used groups of squadron numbers for the aircraft role. Naval Air Squadron (NAS) Nos. 700 to 749 were designated for catapult flights but eventually for training and ancillary squadrons. Similarly, Nos. 750 to 799 were training and support squadrons. The vast majority of these were formed just before or during WW2 and disbanded after the war. Frontline squadrons were numbered 800 to 899 and later 1700 to 1899 although not all of these were formed. Most were raised as carrier-based squadrons during WW2. NAS Nos. 800 to 809 were designated single-seat fighter aircraft (After the war 805 NAS and 808 NAS became Royal Australian Navy Squadrons). Nos. 810 to 819 were designated Torpedo Bomber Squadrons, later Torpedo Spotter/Bomber  Reconnaissance Squadrons (TSR & TBR). The same designation was given to Nos. 820 to 859, although 839, 843, 844, 858 and 859 were not used. Nos. 860 to 869 were reserved for Dutch crews but only two were formed. Likewise, 870 to 879 were reserved for Canadian naval fighter squadrons but only five were used. NAS 880 to 899 were regular FAA single seat fighter squadrons; all used during WW2.
The prefix ‘1’ began once the series ran out but these were all allocated to frontline squadrons. Of the NAS 1700 to 1769 range only five were used, 1700 to 1703 and 1710. Of the 1770 to 1799 range, designated as two-seater fighters, only six were used. From 1800 to 1829 only NAS 1820 was adopted and similarly, NAS 1830 to 1899 were designated single seat fighter squadrons, but NAS 1854 to 1899 were never formed. Many of the 1800 series were formed in 1944 to 1945 in the USA for the Pacific theatre, the majority of them being manned by Volunteer Reserve pilots supplied with Corsairs.
Squadron Codes
  The Squadron code became official after the Munich Crisis in 1938 but there are a multitude of anomalies and discrepancies attached to coding. Ordered by the Air Ministry the standard was to have the two-letter squadron identification with the individual aircraft letter, or callsign, either side of the roundel on the fuselage, usually a letter, i.e. ‘G’ for George. Many squadrons used a selection or all letters of the alphabet for individual aircraft throughout their lifespan. With the outbreak of WW2, some squadrons changed their codes as new codes were being allocated. This led to a large number of squadron codes being utilised resulting in the vast majority of squadrons using multiple codes during their service. Unlike the serial numbers, squadron codes had no restriction on letters used so a great many combinations could be applied. The only exception was the use of letter I which could be confused with a number 1. However, some codes were used by numerous squadrons, e.g. AS was used by five different squadrons. As well as letters, alphanumeric combinations were also used, for example 4H for No. 142 squadron.
The lettering colours were white or medium sea grey initially but standardised by 1941 to Sky for day fighters/bombers, Dull Red for night fighters/bombers, sometimes with a yellow border, and Light Slate grey for Coastal Command.
FAA aircraft used a different system especially with the carrier-borne aircraft. Single letter codes or alphanumeric codes were applied for identification. With a letter for the ship , a number for the aircraft type and a letter for the individual aircraft squadron callsign. Later in the war a three-digit number was applied with the first digit representing the crew number, an American identification code. For example, a Seafire might have 121 A or a Tarpon 324 B. The letter would represent the mother ship.
After WW2 coding was gradually phased out as were the number of operational squadrons. Aircraft were identified by the serial number and increased use of squadron flashes on the fuselage, intakes or nose section, and badges or motifs which were displayed usually on the tail. A single letter or number identified the individual aircraft. The FAA still used letter codes for the carrier on which the aircraft was based with a three digit individual code.