Just bought a 2005 S-Type SE 3L Automatic>
After only a couple of hours driving around town the gears started to grab/jolt, mostly from 2nd to 3rd but a bit from 1st to 2nd. It did it about 6 times over an afternoon, and today 3 times over about 5 miles.

I had an S-type before, and know that you can't put-in transmission fluid/gearbox oil yourself - which would have been my first course of action. Is it knackered?

 

You can DIY - see the threads

But be sure it's not being caused by an engine fault you don't know about!

 

Has the transmission ever been serviced? The dealers usually sold owners on the "sealed for life" nonsense on the automatic transmission, so if you have more than 60K miles on the car, or 5 years, since the last service (or from new) then a service is due. As Jag V8 indicated there is lots of information here on the Forum on the service of your 6 speed ZF transmission,

Here is a JagTV video on the process:

 

In addition to a gearbox service..
Check.with jaguar to see if it's had or needs any software upgrades.
Do a reset on the gearbox ecu to start it learning again but for your driving style.

 

Hey, I know how your feeling right now, I have the exact same issue going on, transmission shop is looking at it on Tuesday, i'll let you know what they say.

 

Is the "reset" where you take off the battery terminals for a while (i did overnight), and then touch the pos and neg together? I did this last night/today, and it didn't throw any gearbox faults so far.

 

You've largely stopped it knowing what's wrong, at least for 2 warm ups.

Hopefully you've not made things worse, but if the OBD monitors don't set then you may struggle to get help via codes and be working somewhat blind.