Here is a post from roadfly about limited slip Ds:
Re: Limited Slip Differential
I know you know alot more about the Jags than I do, but I do believe they have a limited slip rear end. I have had many fast cars that I have built over the year( realtive of course, 65-69 and 79-93 Mustangs) and its quite obvious when cars dont have it. VERY rarely was I ever able to spin both wheels with a non-limited slip rear end, however it is quit easy to do with one. In regards to the XJR 308 I think it just has a "soft" clutch pack(Ill have to get an exploded view to be certain, however Car and Driver says it does have one and so does Top Gear).

Here is what Matt Moran has to say.....




The drag radials that I'm using only work well if you do a burnout before each race. To do this, you need to get both rear wheels spinning. Unfortunately, even though the XJR apparently does have a limited slip differential, the clutch pack in the differential was not tight enough so more often than not, only one wheel would spin. Then, when I went to launch, the other wheel would spin on the line. I eventually found that I could get a custom built racing differential from an XJR-S that would have a tighter clutch pack and could also be made with different ratios. I went with a ratio of 3.55:1 vs the stock ratio of 3.06:1. It didn't make it significantly faster (only about 0.1 seconds over 1/4 mile) but finally my traction problems were solved



So going from 3.06 to 3.55 and LSD was only worth a 1/10th? Has any one else tried this ?

 

If you compare these two cars ( M. Moran and J. Bihari ), you can see that 60ft time difference was just 0.12sec. Moran had LSD with 3.55 ratio, high stall speed torque converter and drag slicks - Bihari , no LSD, stock 3.06 and street/DOT slicks.
2001 Jaguar XJR 1/4 mile Drag Racing timeslip specs 0-60 - DragTimes.com
1998 Jaguar XJR 1/4 mile Drag Racing timeslip specs 0-60 - DragTimes.com