Johnball - there is no myth regarding Jaguars claimed power ratings.
The quoted 1950s/60s Jaguar Power ratings were all accurate and honest, but you need to appreciate they were tested in strict accordance with the then industry standard - which was an SAE GROSS Power rating, and if you want the details of what that means, Google it, but it is an accurate and precise Standard. Essentially it is the power achieved by just the bare engine, in a environmentally controlled laboratory, and a purpose designed and controlled test bed, but it is a GROSS figure, with no losses due to the engine driving any ancillaries, such as generators, and water pumps, let alone clutches, gearboxes and rear axles.
Your CCK Historics will not be doing a similar test, so there is no comparison possible. Once you do a power test on a ‘rolling road’ - it is far removed from an SAE Gross power test as you get a huge amount of losses by the engine having to drive through a gearbox, rear axle, and tyres rolling on a road, so quoted figures will be NET power (of variable accuracy depending on whether done properly or not).
The question that really matters does CCK actually conduct their tests in a fully controlled environment (this can have a significant impact) to a recognised Test Standard? Otherwise the figures they quote are even less meaningful than Jaguars 1950s/60s SAE Gross figures, which can be compared accurately to other SAE Gross tests quoted by other manufacturers and other test facilities.
But the relativity of figures is significant and real. So on its introduction, an XK120 engine achieved 160bhp (SAE Gross rating). The upgraded XK120 SE engine produced 180bhp (SAE Gross), so a real 20 bhp (SAE Gross) improvement. The standard XK140 engine produced 190bhp (SAE Gross), so again another real 10 bhp (SAE Gross) improvement, and the XK140MC (with C-type head) produced 210 bhp (SAE Gross) and so on, up to the 265 bhp (SAE Gross) quoted for a 3.8 litre/straight-port-head/triple HD8 carburetter E-type engine. So the 160 to 265 bhp (SAE Gross) represents a pretty amazing development of an engine that remained road-tractable, acceptable fuel economy, and in a vehicle with satisfactory cooling system to cope.
CCK Historics horsepower numbers cannot be compared with Jaguars SAE Gross figures, but again their relativity to other figures they quote can most definitely be relevant comparisons - subject to one huge qualification. How accurate is their equipment, is their test environment controlled, operator skills, and is test done in strict accordance with a recognised Test Standard. Most private workshops simply do a reasonable test, where they can assess their own relativities, and thus do what you asked them to do - optimise your own particular engine, but I wouldn’t get to hung up quoting numbers in absolute terms to compare against other uncontrolled test numbers; of little value apart from good debate and bragging rights at the local pub.
But still money well spent, if CCK Historics now has your engine running to its optimum (in accordance with your priorities)
Also keep in mind, that when you modify your engine, to produce more power than the original Jaguar solution, its not free. There is a down side that may or may not matter depending on other aspects. XK120s were and are known to have marginal cooling system, and increasing the power of an XK120 engine installation, will add additional load to the cooling system, which may or may not matter depending on how vehicle is used, and indeed where re prevailing ambient conditions.