In England and Wales at that time, as I understand it, a short birth certificate - giving just child's name, date of birth and registration district - was issued to parents free of charge. If they wanted a full certificate - giving details of the parents and a more precise birth location - they had to pay a fee, and many parents didn't bother.
In those days, the short form was sufficient for proof of identity, but since 2008 the long one is needed. Nowadays, parents have to pay for the birth certificate (either short or long) but as they both cost the same (£4), I can't see any point getting the short one.
My own parents' original birth certificates - my father's the short version (1919) and my mother's the long one (1923) - clearly illustrate the difference between the two.