The Edith on the 1901 Census is probably the same one listed on the 1881 Census as their oldest daughter (Edmund & Elizabeth's) born circa 1872.... You have a daughter listed as Elizabeth born 1872 but I believe it was actually Edith.
Edward Brooks, age 54 on the 1901 Census is a mistake by the person who transcribed the census - Edward should have read Edmund - that is actually EDMUND. Your Edmund was born in Oxford circa 1846ish. Your Edmund could not have been born in 1866 as he married Elizabeth in 1870 - if he was born in 1866 he would have only been 5 years old in 1870.
The only Gertrude Lilian/Lilian Gertrude was the daughter - a Brooks - she was not a Foster. I see no marriage for Lilian Gertrude or Gertrude Lilian Brooks - possibly she never married?