"the GRO's indexes are secondary indexes" not "the original indexes held by local register offices", hence transcription errors can occur.
I believe this has been explained many times before. The online GRO indexes have nothing to do with the old indexes. They are currently indexing from the
original documents and any surname in the mother's column will not be indexed if it cannot be determined that the name is her maiden surname. The name must be preceded by the word 'formerly' to be indexed.
The old GRO indexes were different in that they indexed under both surnames if the father was named and mother's name was not preceded by the word 'formerly'. These are the indexes that are used by FreeBMD and this is why you see Ann Elizabeth's birth indexed under both names on FreeBMD but not in the GRO indexes.
B. As the Lombardini one doesn't show on the GRO site, I would email them quoting the reference details for both the Cuttle and Lombardini entries explaining you want the one that has Fanny as the mother. (I'll look again for you though just to make sure)
The correct way to query an entry is to use the link at the bottom of the search page which says:
Noticed a problem with a record in the GRO Indexes?
You can report it to GRO and help us improve the quality of information available.
In this case the most likely answer will be 'Investigated – No amendment required'.
Debra