Here is what I know about mandrels.
Berea (BereaHardWoods Co. Inc.), who was involved in the very early days of developing pen kits, specified the "standard" pen turning mandrel shaft which they later referred to as an "A" mandrel. According to the Berea specification, the "A" mandrel is 0.247" inches +0 / -0.002" inches in diameter. Most bushings are designed to accommodate this size of mandrel.
However, to make supplying mandrels easier, most manufacturers fall back to one of two standard Drill Rod sizes rather than making a custom mandrel that meets the 0.247" inches +0 / -0.002" inches specification. They consist of the "D" sized Drill Rod and the "C" sized Drill Rod. According to your post, I would assume that Axminster has done the same. Size "D" Drill Rod is specified as 0.246" inches +/- 0.0005" inches typical and is a very good replacement for most standard 0.247" inch "A" mandrel shafts. The alternative is "C" Drill Rod which has a slightly smaller diameter of 0.242" inches +/-0.0005" inches.
Although all bushings should fit on the smaller, "C" (0.242") mandrel, I personally, I use the larger "D" Drill Rod (0.246"). For most of the bushings I have, it does provide a better fit; however, when I come across a set of bushings that feel to tight on it, I swap it out for a "C" size. So, I actually use both sizes depending on how tight a particular set of bushings feel.
Regards,
Dave
PS If your Axminster system does not have a threaded mandrel, you could do what I do. I buy 3 foot lengths of "C" and "D" Drill Rod and cut them down to about 12" inches to make my mandrels. Of course, if the Axminster mandrels are threaded, you will likely need to buy a replacement that is also threaded.