For info…. in case it helps anyone else looking
looks as if Edith Smith birth registered as Edmunds
EDMUNDS, EDITH -
GRO Reference: 1837 D Quarter in ISLE OF WIGHT Volume 08 Page 186
That is not correct.
The above birth record is Edith Edmunds - born on 17 December 1837 at Shanklin; father: William Edmunds, Labourer; mother: Jane Holland (not shown as mmn on GRO, just shown as "-").
Mary's daughter (with Charles Smith), Edith Smith, was Christened on 4 July 1837 - civil registration began on 1 July. I too thought the above was Edith Smith, with confusion over the requirements at the very early stage of registering a birth. Unfortunately, it's someone else!