Invented by John Buckingham, a Coventry engineer, the .303 inch Buckingham round was developed early in WWI as an anti-balloon round. Originally round nosed, the salient feature of the Buckingham was that it contained yellow phosphorus and was sealed with a small hole drilled in the side of the envelope filled with fusible metal (a type of solder). When the bullet was fired friction in the barrel melted the solder and on leaving the muzzle the phosphorus started to leak and was ignited by the air.
The intention was that the burning phosphorus would ignite the hydrogen in the balloon as it passed through. The round nose did not work well in machine guns so a Mark II with a spitzer bullet was designed. This worked fine in the guns, but the pointed bullet left too small a hole in the balloon fabric and so did not ignite well. The Mark III was then developed which had a 3mm flat on the nose of the bullet to make a larger hole.
The Buckingham Mark II and III continued in service until the end of the war, but attempts were still made to improve cutting properties of the bullet. A new design with a square shoulder half way up the bullet ogive was developed with the intention that this would cut a round hole in the balloon fabric in the manner of a modern wadcutter bullet, but this was not complete by the end of the war.
Work continued on the design post war and the “Cartridge S.A. Incendiary .303 inch B Mark IV” was introduced in the late 1920s, the “B” code for incendiary ammunition having been introduced in 1927. This round remained in service until at least 1943, although later Marks had been introduced from 1940. Kynoch also made a trade pattern of the Buckingham with a slightly different internal design known as the B Mark IV*z.
The B Mark IV was very successful and was used widely during the Battle of Britain, the distinctive smoke trail of the burning phophorus often showing in gun camera films. As you say, it was also popular with the LRDG/SAS for attacking aircraft on the ground.
Attached is a picture of Buckingham firing his ammo at Hythe in about 1915 and the rounds.
This picture shows Buckinghams Mark I to IV
This one shows l. to r.
Buckingham Mark II (1917)
Buckingham Mark III (1918)
Buckingham B Mark IV (1929)
Kynoch B Mark IVz (1940)
Kynoch B Mark IVz (1941)
(Sorry about duplication in pictures, but they are what I had to hand.