"I was made to believe at the time that if I did not give them the dads surname that he would have no parental responsibilities"
This is very confusing indeed. May I ask who told you this? Was it somebody in some sort of official position or was it just a friend of yours? Unfortunately, this is not true.
"Now I am trying to find a way to officially have the birth certificates re registered with my surname added."
Again, this is quite confusing. Do you not appear as the mother on the birth certificate?
Or are you saying that you want the names of the children altering?
There is a process when there has been an obvious error (eg spelling mistake):
https://assets.publishing.service.gov.uk/media/6788c91c3f1182a1e258a2fa/A._I+-+How_to_apply_for_a_correction_to_a_birth_registration_v1.2+1.pdf
But, even then, the original information will always be shown as it was first given at the time of the registration, but a note will be written in the margin of the register explaining what the correct information should be and the date on which the correction was made. All certificates issued afterwards will include this note.
As I understand things, wanting to add the mother's surname would not come under this. You would need to do deed poll.
"I see it's possible to add a fathers name at a later date...but not the mothers"
The reason for this is that a mother can register the birth of a child without naming a father. Indeed, if you are at all into studying your family history, then this was very common even up until the 1940s and 1950s that if an unmarried woman gave birth to a child then the name of the father would not be recorded on the birth certificate (even if she might wish it to be).
The whole thing about adding a father's name at a later date doesn't change the name of the child in any way (that still has to be done through a deed poll) but it simply adds the name of the father to the birth certificate so that the child might know who their father was. The original information is still there with a note in the margin