Ann, I have been looking at Mary and Rose on the 1881 census in the orphanage, and the birthplace for both girls is shown as London.
There is an Archer family at Hilton, Burton on Trent, Derbyshire on the 1881 census with head Robert, wife Mary, and children including Agnes M age 3, so it looks likely that she is the Mary Agnes Archer born in Burton on Trent in 1878, not your grandmother.
If you would like help tracing your grandmother, it would be best if you can start a new thread rather than continuing with it on Marg's threads as it looks unlikely that there is a connection between your family and hers. If you would like to do that, the link below will take you to the Research Questions board, and then just click on the "New Thread" button:
http://www.genealogistsforum.co.uk/F...isplay.php?f=4