When I do a kick down in a 00 XJ8 Sovereign. It seems to be hesitant and the same when you kick down when the S button is engaged. If you build up the speed gradually, then kick down it seems ok

Low fuel pressure

If it is cranking fine but not firing then you have a fuel problem. Maybe the fuel pump, filter, injectors...etc.

Check and clean mass air flow sensor according to directions on can. BE VERY CAREFUL< THIS SENSOR IS VERY DELICATE. Hope this helps.

http://www.ebay.com/sch/items/?_nkw=2001+jaguar+xj8+owners+manual&_sacat=&_ex_kw=&_mPrRngCbx=1&_udlo=&_udhi=&_sop=&_fpos=&_fspt=1&_sadis=&LH_CAds=&satitle=2001+jaguar+xj8+owners+manual

sounds like the torque converter is going out...I remember on some of the xj8 and xjr models in the x350 class had these issues...the signs were a surge in the rpm cluster at about 50mph and when you attempt to pass or kick down it will ****....but as you get higher in speed it eventually smooths out...This is my insight for your issues...If it was the transmission control module it would throw a definite code.....Usually this issue with the converter was with the earlier vin models ranging in g00 to g400 numbers....and a few others

I have the same problem few days ago, and still didn't find any solution. Can any one please help?????

Sounds like freon is low/or has moisture in it and is having to build up pressure before engaging.

you could need a bigger tranny cooler, plowing is tough on a transmission, get an after market cooler.

I've had the same problem on my 2001. It turned out to be the battery. Apparently the voltage had dropped to the point that the computer began to malfunction. I'd first go to a battery shop and have it checked under load before looking for other solutions.