Given the fact that Alfred was adopted by another family and the fairly unusual surname, it may be worth looking at Elizabeth (born c 1865 died 1886) and Henry Weedner (born c 1862 died 1890) both in Stourbridge/Birmingham area as possible parents or at least relatives?
There is a newspaper account from 1886 in relation to Elizabeth's death, which refers to her husband being called Henry (an umberella mender) and also to two young children (although it is not entirely clear whether these were her children or her sister in law's children). If you PM me I can send the newspaper accounts.