I’ve examined the two tool posts and can confirm the following.
Axminster: Stainless Steel post with M12x1.25 thread. Thread depth 9.0mm. The collar below the threaded section is, on the example I measured with a micrometer, 14.1mm diameter and around 5.9mm deep. Spanner flats are a little under 19mm.
Robert Sorby: Non stainless steel post also with M12x1.25 thread. Thread depth 9.4mm. The collar below the threaded section is 14.85mm diameter and around 4.9mm deep. Spanner flats are a little under 22mm.
This means that Robert Sorby Rests will fit both Sorby and Axminster tool posts. Due to the smaller recess though Axminster Rests will Not fit the Sorby post.
Note: M12x1.25 is a fine thread.
M12 threads are commonly available with 1.0, 1.25, 1.5 and 1.75 pitches.