I downloaded your dwg and took a look. The dwg loads fine for me (Pro 2.3). The problem is the CAD file is not in OSGB36.
OSGB36 is a geographic coordinate system; so the coordinates are decimal degrees (geographic) coordinates. Those coordinates in the DWG are certainly not OSGB36 because they are clearly in a projected coordinate system, that is, in meters or feet, not degrees. To have things plot in the right place (since your dwg file has no coordinate system defined) you need to find out what the xy coordinates are, and set the map coordinate system to it. If the coordinate system you set for the map matches the cad file's xy values, the basemap will appear to line up under your CAD linework.
You may want to check this out again too, but you definitely are stuck until you find out what the XY coordinates in your DWG file are.
Map units, location units, and display units—ArcGIS Pro | ArcGIS Desktop
I hope this is helpful.