Trouble changing 'unknown' CRS of vector layer in QGIS

I’m new to GIS. I’ve been given a shapefile that I’ve added as a new vector layer in QGIS and it displays OK, but it says it has an Unknown CRS. The CRS from the prj file is:

PROJCS["Transverse_Mercator",GEOGCS["GCS_Airy 1830",DATUM["D_unknown",SPHEROID["airy",6377563.396,299.3249753150316]],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]]

and the one displayed in the details window of the CRS selector is:

Unknown CRS
WKT
PROJCRS["Transverse_Mercator",
    BASEGEOGCRS["GCS_Airy 1830",
        DATUM["D_unknown",
            ELLIPSOID["airy",6377563.396,299.324975315032,
                LENGTHUNIT["metre",1,
                    ID["EPSG",9001]]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",49,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",-2,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",0.9996012717,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",400000,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",-100000,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
Proj4
+proj=tmerc +lat_0=49 +lon_0=-2 +k=0.9996012717 +x_0=400000 +y_0=-100000 +a=6377563.396 +rf=299.324975315032 +units=m +no_defs +type=crs
Extent
Extent not known

I’d like to convert it to a well known CRS within QGIS but when I do select a different CRS from the options, all the features disappear, with the exception of EPSG:3994 which displays the right map but inverted N/S. Does anyone have any advice on what I’m doing wrong or what CRS I should be changing it to?