Birth certificates from the GRO for that period of time cost £11.00. This is her birth registration from the GRO
FROST, SYLVIA JEAN -
GRO Reference: 1933 S Quarter in EXETER Volume 05B Page 92
The little dash means that she was illegitimate so the surname is the same.
If you haven't used the GRO before you will need to register first.
https://www.gro.gov.uk/gro/content/Click on Order Certificates Online and then register. When you have done that you can then go to the Search the GRO Online Index section, on the right hand side. Click on the birth section then fill in the name etc, put in Exeter for District of Birth and then click on the little white button to the left of her name. You can then go through the order process.
The GRO is the best way of ordering certificates. There are other websites through which you can order certificates but they are much more expensive. If you get stuck do ask for help.