Ladylinda,
Oh bless your heart!! I was just beginning to think this morning I should hang Martha up as my token "brick wall".
Yes, that is her on the 1911 census! And I've been searching with the wrong spelling for Gardiner all this time too. She's apparently disposed of poor little Charlie from her marriage to Herbert somewhere (the other two boys she packed off to the Middlemore Home, and they were sent off to Canada in 1904). And she's shaved off some years -- she was actually born in 1872, not 1875.
And you found the birthdates for Arthur and George too!
For the 1901 census, her husband, Alfred Herbert, was in the city hospital, ill with typhoid fever -- he died shortly after the census was taken.
Her son Alfred, born from that husband, came along before they actually got married, and his birth is registered under her previous married name, Brinkworth. She very cleverly gave him the middle name of "Herbert" though, and then when she married his father, she dropped his surname Brinkworth. She seems a bit of a devious sort!
Thank you SO much for all the time and effort you put into searching for me. You've helped solve a mystery I've been working on for a long time.
Best,
Ann