I have not got access to the 1911 Surrey census so I cannot answer your question. I have however looked at what I think is your family in 1901, from which I presume that you have quoted Elsie's DoB. Her age on that may have been transcribed as 11 but I think that is was only 4 as one stroke of the pen seems to have faded. This will give her birth as 1896/7, she could be the Elsie Ellen Collins, registered in Farnham District, June quarter 1897, Volume 2a, page 124.
As mother Ellen was only 24 at the time it would be unlikely that she had a daughter of 11.