When I created my base, I realised that because of the orientation of the original object meant that the axes were in the center of edges, rather than lining up with vertices. To correct this I rotated it by 11.25 degrees.
This created a problem when applying the mirror mod, as the mirroring was also off by 11.25 degrees. The solution I found was: in Object Mode, to go to Object > Apply > Rotation. This sets the rotation back to 0,0,0 but changes the vertex data so that it effectively stays in the same place.
Not sure if this is the “correct” solution, but it sorted out my problem. Of course it wouldn’t have taken long just to rebuild the base, however I wanted to find a fix that would work if I found myself in the same position with something I’d spent a lot of time on.