Tip tinner cleaner is still readily available. e.g. Maplin stock it in-store as JG06G. However I'd bet you can get it cheaper from your preferred distributer with your next order.
Overheating a bit causes this sort of problem so your tinning procedure is at fault. With the bit hot enough to melt solder, wipe off as much as possible of te excess solder with a dry paper towel folded into a thick wad, then tin only the face and just round the edges for chisel and screwdriver tips or just the last 5mm for conical tips using a cake of tip tinner cleaner and a light scrubbing motion. Do NOT dig it into the cake.. If you cant get it to take solder without balling up, then the oxide layer will need to be removed with mild abrasive (I prefer a fibreglass pencil, used with the tip hot) but the iron plating is very thin, and if the abrasive breaks through exposing the copper core, the tip will rot away due to the solder dissolving the core within a couple of days use, hence my recommendation to order a spare tip. For through hole work, chisel tips are preferable to conical ones as you get a larger working face with better heat conduction to it.