Hi Peter, which model MV have you got?
I assume you mean left to right as in side to side, not rotational ?
If that's what you mean, no it should not move left to right, remove the nut retaining clip and see if that nut is tight.
Most of the time the sprocket will have rotational movement when the rubbers are worn, and you will be able to see this quite easily.
Time for strip down Peter, take some pics, but I recon you have sprocket/carrier replacement due.
Another member just did his and got parts from forum vendors at great prices.
Some pictures would help though, even just to confirm that you're still using the 750 style sprockets.