I have now designed two styles of buggy mitt, the original for the hook handles and now a second for the pram style handles.
The first slides over the handle, you can then hold the buggy handle inside the mitt and easily remove your hand to respond to your bay, replacing a dummy etc and the mitt stays in place-no more holding a glove in your teeth or getting home to find one missing!
The pram style fastens around the handle and again you can remove your hand and leave it in place.
Both have a knitted lining for extra warmth. I haven't added a waterproof inner as I am expecting wet mitts to be dried like a normal mitt-possibly on a radiator and didn't want to extend the drying time needed but can add a waterproof inner on request.