“W” is the British code for armour-piercing. Its origins are in WWI and originally stood for the Woolwich Arsenal type of .303 AP but was afterwards extended to all British small arms ammo.
Other common British codes are “G” for tracer, “B” for incendiary, “D” for drill and “U” for Inspectors rounds.
The green primer seal is another ID for AP ammunition. I mention this only because you occasionally see a British load with the wrong headstamp, probably done to use excess cases. But, they will have the correct color code for the actual load in the case. I had a couple of these during my .303 and 7.9 x 57 collecting days, although I don’t recall now the exact examples. I recall one had a purple seal (ordinary ball) on a case with the “W” for AP loads, but I don’t recall now whether it was a .303 or a 7.9. I do recall that overall cartridge weight indicated the primer seal color was correct.