The problem with the XJR-S is that the factory claimed numbers do not match the actual observed performance of the car. In US trim, it was nominally rated at a standard 313hp for the early cars and later 328 (318 and 338 for Euro trim), but some people have gotten more than that at the rear wheels on a dyno. Also, a 313hp or 328hp engine will not make a heavy XJ-S do 0-60 that fast (spec was 6.5, many are faster, some do it in 6 flat), not with that TH400 automatic transmission and 2.88 rear diff ratio (top speed was a nominal 158mph, so they didn't get acceleration at the expense of top end). For comparison, my former 2000 XKR was 200lbs lighter, a lot more aerodynamic and had a nominal 57 horsepower advantage as well as a more favorable gearbox and rear diff ratio - and it was only about a second faster to 60 (5.3 sec) than the XJR-S. The later 6.0L XJS (different 6.0L variant) made 308hp in US spec, has the 4L80E transmission and a much better (3.58) rear gear ratio, and it is about a half to a second slower to 60 than the XJR-S (6.9 seconds). Which tells us that there is no *way* that the 318hp/TH400/2.88 car should be faster if everything is as claimed.
And, of course, TWR would tweak them to order, like Aston would do to their cars. They were all fitted with a specially programmable Zytek fuel injection/engine management system, so it was relatively easy to optimize a particular car with a custom fuel map. Additional power was just a note on the order form away, should you want it - along with many other optional performance-enhancing features. Every XJR-S was built to order and no two are the same in any respect; they really were bespoke Jaguars by way of TWR/JaguarSport.
From what I've been able to find, the average XJR-S left TWR with somewhere around 380 real horsepower and 400+ lb/ft of torque, with even more available through judicious tuning at TWR.