Just following up on this with some progress in case anyone else comes up against this problem.
I worked out that when I brought the tiff into ArcGIS the coordinate system had not been been properly applied to the layer when exported from Reality Capture. It was ‘unnamed’ and as a result it had used the wrong spheroid (WGS instead of Airy 1830), which would be sufficient to send the layer 50m in the wrong direction. If I manually defined the projection of the ortho tiff in ArcGIS as British National Grid then it plotted correctly.
The big question here then, is why the exported ortho doesn’t have the coordinate system properly applied when it works fine for other kinds of exports (obj for example).
It’s fixed for now using this workaround, but it’s an extra step I will have to take with all my models in this system.