I've only just joined and come across this thread. I think some of the schools mentioned are much later than the period you are looking at. I think Ellington opened about 1932. I think St Lukes was probably later as well. The only schools I know of in 1903 were:
National Schools, East Street
Wesleyan Schools, King Street
Boyn Hill Schools
St Pauls, Albert Street
British Schools, West Street
Braywick School
Roman Catholic School, Cookham Road
West Street Council School (from 1904)
Brock Lane Council School (from 1904)
Hope that helps