That canopy design doesn't look like a fighter at all (maybe some lightweight fighter based on a trainer a/c), and the engine apears to be an air cooled inverted inline (Argus or Hirth) possibly a real a/c (or close to one) but not a fighter.
I'll check a bit. (I beieve several bogus planes were used on the other Indiana Jones movies as well, so it wouldn't be surprising, but most of those resembled real a/c as well iirc)
I had an inkling that it was a Swiss trainer, then I found it, the Pilatus P-2, it only seems to have been altered by having fake 'DB601' type exhaust stubs stuck on the cowling.
I think I found it, not a German a/c at all, though some used German engines (Argus As 410) and some design components from German a/c. (Bf 109's landing gear)
The British Specification F11/37 was for a twin engine, 2 seat fighter capable of day night operations, in a fighter or ground support roll.. Armed by 4 20mm canons housed in a power operated turret. The specification called for an aircraft capable of 370 mph at 15,000 ft, with a service ceiling of 35,000 ft with an endurance of 2.5 hours. The Aircraft was to be armed by 4 20 mm canons with 240 rounds of ammunition a single 250 lb bomb carried internally.
Boulton Paul P92 was designed to meet this specification it was this company that the contract was awarded to. Serials L9629 L9632 being allocated to the two prototypes. Heston Aircraft built a half scale model of the P92, called the P92.2. The serial V3142 was allocated to the P92.2, which was flown during May 1941. With the cancellation of the P92 project the P92.2 was stored for some time before eventual scraping.
At the time of Munich Bristol proposed using Hercules engines on a new aircraft using mainly Beaufort components, this design was eventually called the Beaufighter.
I thought the framed glazing was of the (rather large) canopy. And if it's German those aren't necessarily radials, the Jumo 211 and 213 looking like radials (save the exhaust ports) due to the use of an annular radiator and radial-type cowling. (with a couple exceptions, like the Ju 87, with a chin radiator Jumo 211)
And a bit late, but Graeme wasn't the Bristol 153 a single-engined fighter design?