Apologies in advance though thought the following was relevant given the Jaguar Mark 2 formed the basis of the Daimler V8 engined variations.
Anyway beyond the 1954 military engine, the Daimler V8 and the unbuilt V12-based V8 is it known what other V8 engine projects Jaguar experimented with during this period (or even prior)?
Given Jaguar was looking to build upon its success it is surprising they never thought about developing an in-house V8 project aimed at the US.
Armstrong-Siddeley for example allegedly developed an 200+ hp 4.6 V8 (with Twin-Cams envisaged though not necessarily implemented) derived from a pair of Sapphire 234 engines (and also looked at a 2.7 4-cylinder derived from the 4-litre Star Sapphire 6-cylinder, which would have in turn potentially allowed for a 5.3 V8) prior to ceasing car production.
What prevented Jaguar from taking a similar approach to Armstrong-Siddeley in creating in-house 4.6-5.0 (roughly 4588-5040cc) V8s derived from the 3.4-3.8 XK6s via a pair of XK4s (or XK6s minus 2-cylinders)?