This is what is expected by ArcGIS:
PROJCS["British_National_Grid",GEOGCS["GCS_OSGB_1936",DATUM["D_OSGB_1936",SPHEROID["Airy_1830",6377563.396,299.3249646]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",400000.0],PARAMETER["False_Northing",-100000.0],PARAMETER["Central_Meridian",-2.0],PARAMETER["Scale_Factor",0.9996012717],PARAMETER["Latitude_Of_Origin",49.0],UNIT["Meter",1.0]]
This is what your feature class contains:
PROJCS["British National Grid",GEOGCS["Ordnance Survey Great Brit",DATUM["Ordnance Survey Great Brit",SPHEROID["Airy 1830",6377563.396,299.3249646]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",400000.0],PARAMETER["False_Northing",-100000.0],PARAMETER["Central_Meridian",-2.0],PARAMETER["Scale_Factor",0.9996012717],PARAMETER["Latitude_Of_Origin",49.0],UNIT["Meter",1.0]]
ArcOBJECTS and the File Geodatabase API compare these strings and since yours is seen as different, it is seen as "Custom".
What was the source of this data and how was it loaded?