Early 20th century (most likely)
Martha was a Muggle girl who worked at Wool's Orphanage in the 1930s. She worked at the orphanage during Albus Dumbledore's visit to Tom Riddle, when the latter was eleven, by which time she was looking after children who had chicken-pox. Martha worked at the orphanage from a time before Tom Riddle was born to sometime after Tom Riddle went to Hogwarts School of Witchcraft and Wizardry at the age of eleven.
The name "Martha" comes from Aramaic מרתא (marta') meaning "lady, mistress".