Having looked at Colin's larger copy of the first 'photo a Morris still looks favourite. The body style is usually referred to as 'two-seater with dickey'.
The general radiator shape seems correct. On zooming in a bit on the mascot/gauge it is not as tall as it first seems (I think there is a reflection or glare in the radiator top).
The two pictures show the Dickey seat on a 1926 Morris Oxford and a Morris Cowley. Although this is a larger four-door version it shows the radiator clearly. The Cowley and Oxford models were essentially the same the differences being in trim and engine sizes.