The Longworth chuck works well in principle but locking it could be difficult. It's a nice bit of engineering and sliding the jaws open with a simple turning action is quite satisfying, but getting it to stay locked so that it's strong enough to grip some material while spinning in a lathe might be quite tricky.
So far Robot Steve has come up with some sort of torsion spring to keep the jaws clamped around the piece. We'll give it a try, but we'd also like to try a lower-tech solution:
At BuildBrighton, we've access to a Myford lathe. So machining a piece of rubber with a number of decreasing sized circles shouldn't be too difficult. Exactly the same "chuck" could be mounted on the motor part of a miniature lathe, and also on the free-spinning end, and the two ends drawn together using a threaded rod (or similar) on the base.
By turning the threaded rod, the two ends can be pulled together or separated to fit the length of material to be turned. And by using exactly the same "rubber cups" for both ends, we shouldn't need to worry about centring the piece - so long as we're starting off with a piece of round material (or at least, regular material, consistently thick along it's length) by simply pushing the piece into the appropriately sized cup cut-out, it should automatically be centred.
That's the theory anyway.