This could be a different explanation.
The census actually shows she was born in Upper Chute, Wiltshire. I searched on the 1871 census for a Louise born in Upper Chute and found Ellen Louise Large, born Chute, Wiltshire in 1867. There is a birth of an Ellen L Large registered in Andover in September 1866. If you search for Upper Chute on Google, it is in the Andover district, so that is probably the correct person.
However, I cannot find a marriage to Edmund Webster. The chances are they weren't married. My g.grandparents in 1911 said they had been married for 28 years, which conveniently took them to the year before my gran was born, but no-one has ever found a marriage for them.
Buying a birth certificate won't necessarily help as on my gran's birth certificate, her mother gives her maiden name, then her previous married name (the husband apparently drowned at sea) and then her "new married name" which was obviously the same as her "new husband".
By the way, Ellen Louise's father was a Richard Sheppard Large. You can find him in Purton, Wiltshire in 1851 with his parents etc. 1861 with his wife and children (pre Ellen Louise birth) and on the 1871 census when they had moved to Hertfordshire.
I think Richard may have died before 1871, as on the 1881 census his wife is shown as a widow and a farmer, living back in Wiltshire. Richard had been a corn dealer so probably wealthy enough for his wife to buy a farm of 60 acres. I can't find Ellen Louise in 1881 though.
Lizzie