Birth certificates are in the public domain. Anyone (who knows your name and your approximate date of birth) has the right to obtain a copy of your birth certificate. There's no great risk of ID fraud because organisations which might want to see your birth certificate (such as a bank when you open an account) know just how easy they are to come by and therefore always require additional documentation as well.
It will cost you £11 to get a replacement certificate if you can find the GRO index reference number yourself (see link) or £14 otherwise:
https://www.gov.uk/research-family-history
(I'm assuming that you were born in England or Wales. Follow the relevant link from that page if you were born in Scotland or Northern Ireland).
Follow the HM Passport Office complaints procedure to seek compensation for what you've had to pay out:
https://www.gov.uk/government/organisations/hm-passport-office/about/complaints-procedure