It is confusing, but the 4 girls (Fanny, Helen, Alice and Margaret) appear to have been daughters of Margaret WILLIAMS. That is how they appear in the census records for 1851 and 1861 and 71.
When she baptised them there were given the surname WILMOT.
Another child was born to Margaret in 1867 - Amy Williams
.
It is not clear where the WILMOT name comes from at this stage.