There is a chatter from the clutch that goes away when I depress the clutch pedal. If I stick a screw driver on the clutch, through the filler hole, I can move it laterally around 1-2mm. Before I drop the oil and remove the clutch cover, can someone confirm that this movement is not normal please?
And some idea of what to look for if I have to take it apart would be helpful

spigot bush not fitted or damaged?

You don't want to see this:


clutch

Quite an extreme example of basket wear.

Also check the 'fingers' on the plates which engage in these slots for corresponding wear.

1-2 mm is quite a lot of movement, so you should see something obvious.

Very often the cause of the clutch chatter is nothing more than poor carb balance or mixture adjustment. Kawasaki engines are very prone to this due to the chain that links the primary drive. pulling the clutch in or just taking the slack out of the clutch will make the noise go away but the engine is still a bit lumpy at idle. raising the speed of the idle will have the same effect as you will be smoothing out the uneveness of the idle. if this is the case, no amount of stripping will cure the problem. balancing the carbs really well and adjusting the mixture screws will.

Thanks for all the replies.
Clutch is stripped, no wear visible at all, the basket has a small amount of play, not near as much as I thought feeling through the filler neck, the centre is rock solid. However the plates have blued, to varying degrees , although they are not warped and no sign of clutch slip, so they will have to go back in until I have a new set.
I think cosmick may have a point, the car is going into Autotronix at Dinnington, next Tuesday, for the carbs to be set up.
The idle is not good, and needs 6 turns out on the needles to get it rich enough to idle, not very smoothly, and it feels like it's on 3 cylinders up to 4000rpm, a sign that the primary jets are too small, or so I have been told.

You shouldn't need to change the primary jets as a result of fitting a Bike engine into a car. If it is running poorly it is more likely that the carb jets are resticted in some way, usually by stale fuel laquering the inside of the jet thus making it smaller. it is a devil to remove and often needs a wire pushing through the jet and moving it back and forth to clean the hole. If it runs badly and sounds like it is on 3 cylinders then for sure the clutch will rattle badly and will be very noisy. don't do anything to the engine until the carbs have been cleaned and balanced.

Had the carbs set up yesterday at Autotrinix , they couldn't find anything particularly wrong with them, all the jets as standard and clean, but running very weak at the lower rev range and only 124 bhp at 9200 rpm. They reamed the 38 idle jets out to 40 and now running like a clock with 136 bhp at 10500 rpm
On the minus side, still a little noisy around the clutch, but may be the way of the ZX9R engine?
Big plus is vast improvement in drivabilty, no need to rev to 4000 to stop it stalling, no bogging and pulls away from 30mph in 6th.
Big thumbs up for Autotronix, well worth the £96.

I think its generally a quirk of the BEC to have drivetrain noise. I remember the first time I changed up into second I thought the clunk meant the box was shagged

ZX9's are very notorious for having lumpy idle and very noisy valve train. Is the chatter just there when clutch is out in neutral? or does it do it in gear as well?

What idle speed does it run at? It should be 1200 or there abouts.