For most of the world EPSG:27700 is defined as:
PROJCS["OSGB 1936 / British National Grid",GEOGCS["OSGB 1936",DATUM["OSGB_1936",SPHEROID["Airy 1830",6377563.396,299.3249646,AUTHORITY["EPSG","7001"]],TOWGS84[446.448,-125.157,542.06,0.15,0.247,0.842,-20.489],AUTHORITY["EPSG","6277"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4277"]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",49],PARAMETER["central_meridian",-2],PARAMETER["scale_factor",0.9996012717],PARAMETER["false_easting",400000],PARAMETER["false_northing",-100000],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Easting",EAST],AXIS["Northing",NORTH],AUTHORITY["EPSG","27700"]]
while for ESRI it is defined as:
PROJCS["OSGB_1936_British_National_Grid",GEOGCS["GCS_OSGB 1936",DATUM["D_OSGB_1936",SPHEROID["Airy_1830",6377563.396,299.3249646]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",49],PARAMETER["central_meridian",-2],PARAMETER["scale_factor",0.9996012717],PARAMETER["false_easting",400000],PARAMETER["false_northing",-100000],UNIT["Meter",1]]
Copy the second one into your shapefile's .prj file to make ESRI recognise it.