Welcome Tony,
Ideally there should be no play at all. These rods control rear tracking toe angles. Any play will cause the rear wheels to move around and tyre wear and handling will suffer. Tea trolley like characteristics will become apparent. Besides movement, you should check gaiter condition. Rods fitted with white gaiters seem to disintegrate through UV attack worse than black coloured material. Jaguar have on some models fitted metal shields over the ball joints at the outboard ends which goes some way towards helping that issue.
The joints are the same construction as the lower rear wishbone bushes and damper bushes found on these cars, namely being of the ball and tube type which allow for rotation and radial alignment. This is necessary to allow for geometrical movement as the suspension rises and lowers in service.
Rod removal is not that difficult. Take out the long vertical bolt which links the rear hub carrier and the outboard end of the rod. You then need to get to the inner end which links to the subframe near the centre line of the car. A nut is fitted at that end. You will find it will be able to be partially undone along the stud on the inner end of the rod before it jams. The thread on the rod is de-pitched to stop the nut coming off in service. Use a hacksaw or grinder with a slitting disc to cut through the threaded stud. With the nut and part of the rod stud cut off, the rod can then be taken off the car.
Take the old and new rods and adjust the length of the new rod to a length that is identical to the old unit. That will ensure you keep the original tracking toe angle. Fit the new rod to the car.
If your existing rods are defective, I suggest you replace both rods at the same time. If one is defective, the matching component on the other side of the car will not be far from being in the same condition. These rods frequently need replacing by around 85k miles. Few last longer. The current best prices for new rods currently appear to be £60 for a pair. See this link.
http://www.ebay.co.uk/itm/JAGUAR-XK-200 ... 1305724629
The 2002.5>, X350 and XF all share the same suspension components. All are interchangeable.
Go to the suspension sections on the X350 and S-type sections of this site and view some of my other posts on the subject. Most are illustrated which will help you further understand the workings of this type of suspension.
This link for your interest is for the replacement joints to be found in lower rear wishbone components. They allow for economical refurbishment of the lower rear wishbone arms. The parts are not available from Jaguar who will only sell you new arms at huge prices.
https://www.google.co.uk/url?sa=t&rct=j ... GehwckCnCg
Hope that helps.
Mike K