I think you're right about the mis reading/typing. Now I see it enlarged as you sent it thru' - I could imagine someone reading it as 'House, Jame at Hamel'. So I'm back to 'found at Kennet House.'
If they found her and took her in, do you think there would be documents....also, if they didn't formally adopt her, I'm sure I read somewhere that all births had to be registered in Scotland from 1854. I'm sure she would need her birth certificate for various official thing in later life. I know she went to France in 1919 to visit The Menin Gate (her eldest son was killed in the Ypres Salient) - so I'd have thought she needed a passport for that.