McFly - I think you might need to clarify what you mean by “play” in the sprocket.

If you grab the sprocket with both hands at 9 o'clock and 3 o’clock and pull and push alternately with your right and left hands and it waggles, or has play, then it is the sprocket carrier bearing that is at fault.

If what you mean is the that sprocket turns some distance before it engages with the rear wheel, then (like Nick suggests) it is more than likely the cush rubbers and knackered.

Both are linked; more often than not, the sprocket carrier bearing fails because the bike has been ridden for a long time with badly worn cush drive rubbers.

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