Thanks Dave that makes sense. You found the baptisms of three of the children I have struggled to find any births for any of the children of Mary Elizabeth on GRO. So can't see if they were born as Mitchell or Hitch* If Charlotte or William had requested the change it would mean there were aware that their surname was incorrect.

Helen, The birth of Mary Elizabeth's illegitimate child Ann Eliza HASTROP is on GRO Index in Q4 1871. There is no birth reg for any of her other children
DAVE