In AcrCatalog, right click on your table, click create Feature Class, and use Geographic Coordinate System\World\WGS 1984 for your new shapefile.
Open a new map, and use the British National Grid as the coordinate system. Insert your new shapefile.
Open the attribute table, add new X and Y coordinate columns in your new shape file.
Right click on the new "X" coordinate field and click Calculate Geometry, and use the coordinate system of the data frame. Do the same for the new "Y" field.
Your new shape file now has the Lat Lon and BNG coordinates. Export the shapefile, using the same coordinate system as the data frame.