Took a while, but I had to check the construction of the P100 headlamps (which wasn’t easy). Furthermore, this may now have become an item for the “Saloon” forum. But may be also interesting for the XK people.
As far as I now understand, the situation is as follows:(please correct me if I’m wrong).
The SS Jaguar 2½ and 3½ Litre (1939 – 1940) and the Jaguar 2½ and 3½ Litre (1946 – 1948) had headlamp Lucas 50163A P100LS-EDS which is placed at LHS front (on RHD cars). This is an electrical dipping headlamp. Bulb holder is 509684 for a 12V 60W single contact bulb Lucas 87 with cap BA20s (20mm cap diameter or about ¾”), indicated as a (non-British) “Bosch” cap by Lucas.
At the RHS front (on RHD cars) the headlamp Lucas 50164A P100LS is placed . This has same bulb (holder). The Lucas bulb 87 looks like this:
Replacing Lucas headlamp P100LS-EDS 50163A, Lucas introduced on the Jaguar 2½ and 3½ Litre 1947 – 1948 the same headlamp with a new reflector coded 50307A for Export. It used same single filament BA20s bulb Lucas 87 (12V 60W).
On the later Jaguar 2½ and 3½ Litre versions (Lucas indication 1947 – 1948; possibly for Export?) another P100 headlamp was available with code Lucas 50489B P100L with bulb holder 504801 for a double contact bulb. This is a headlamp without electrical dipping: dipping now obtained via switching between 2 filaments. No bulb was supplied with these headlamp: probably to be acquired locally. This headlamp was placed at LH and RH front on RHD cars. This headlamp was suitable for bulbs with BA20d cap like the 12V 35/35W bulb with Lucas code 80 (later replaced by Lucas 182).
Note that this lamp had a shield above the dipped filament: see picture.
Don’t know exactly which version you have, but the 1947-1948 versions should be suitable for placing a “shielded” bulb although of the (European) type BA20d. The difference in construction between the early and the later P100s only relates to the bulbholder 504801 (double contact) that replaced 509684 (single contact).
If you want a BA20d 35/35W bulb with shield, these are still available in Europe (also with 45/40W or even in Halogen version). Just let me know.