The 1912 Kellys directory (which refers to 1911 as 1912 was publication date) lists E.W.Willard & Co Ltd, carriage lamp manufacturers, as at 187 Newhall St.
The 1913 Kellys (which would refer to 1912) lists their address as 151 Charles Henry St..
The 1915 edition lists them at 151 Charles Henry St.
In the 1921 edition (referring to 1920) E.W.Willard have disappeared, but Willard & Wallis Ltd, motor body fittings manufacturers has appeared at 151 Charles Henry St.
So it does look as if they are the same firm (possibly after a merger, though there is no Birmingham firm named Wallis in that sort of trade listed in the 1915 Kellys)