I'm not sure if this is any help, but my husbands paternal grandmother was called Alice Rainbow and she lived in Long Ditton, Surrey (very near Hampton Court). She died in 1995.
We think she had at least 9 siblings and may have been named after her mother. It sounds as if the Alice you are looking for could be her mother?
Her ancestral name was Reinbeau.
I hope that helps! Good Luck.