Go and read the FCO link. They are NOT birth certificates. Bigbadbarry has confirmed they are however identical in appearance to a UK birth certificate. You do not need these FCO birth registration documents to apply for a British passport abroad or in the UK, FCO staff are officially encouraged to discourage people from the expense at in most cases they are not necessary at all. You don't need them to register for UK child benefit either. All that is needed for child benefit is a valid national document ie passport / national ID card, 1951 refugee document PLUS the proof that one of the child's parents is now living in the UK, irrelevant where the child is actually living (goodness this little known fact is taken advantage of frequently by families who "borrow" children and their national IDs in order to obtain child benefit for children who are not theirs, but UK government being too underfunded that checks on these children's parentage who are living often on the other side of the world are simply not practical and the child benefit is paid for "fake" children).
RockStock ... if your daughter is born in Spain or outside the UK and has been given a British passport, then she is British by descent (few exceptions eg forces children treated as if born in the UK). Her dad (unless he is an exception) would not be able to confer his British nationality on your daughter as he would be British by descent and not from being born in the UK, so British by descent can descend only one generation. So you are British from being born in the UK, so you can confer your British nationality on your daughter and any other children by descent, if they are born outside the UK. If you give birth to any future children in the UK, they will be British by birth in the UK and they can confer their British nationality on any of their children. Hey it is complicated!
In summary, your daughter is British by descent and not by birth in the UK. She cannot confer her British nationality on any of her subsequent children, if they are also born outside the UK like she was. However, she could then move to the UK with her children born outside the UK and before the age of 18, they could under certain conditions then apply for "registration" as British citizens, so long as it is done before they reach the age of 18. Your daughter can also give birth in the UK and then those children will become British at birth automatically, without the need to "register" .
Here's a well written and accurate summary of British nationalities laws.
en.wikipedia.org/wiki/British_nationality_law#Children_born_abroad_after_1982_to_British_mothers_or_to_British_fathers_before_or_after_1983