When I am using my Kelly Kettle I keep the cork clean by hanging it on a little "Y" shaped stick (like a fishermans rod-rest) next to the kettle. This keeps it off the ground and less likely to pick up dirt or get trodden on. Lets face it, you're pretty well guaranteed to havea supply of little sticks to hand if you are using a Kelly !
I contacted the Kelly Kettle Co. some while ago to suggest the possibility of a made-to-measure water carrier that fitted inside the flue of the kettle and/or a screw cap for the kettle itself so that water could be carried in the kettle without danger of leakage. I realise that a screw cap would prove even more dangerous than the cork if left in whilst the kettle was lit, but as people have found to their cost, even leaving the cork in can prove very painful. I was not aware that the kelly used to be available with such an inner container. The reply I got from the K.K Co. gave no indication that they had once sold them, but stated that they may look to produce them "in the future"...