Hi,
I had this problem too. Threw out my GCSE certificates during a house move thinking I'd never need them. 10 years later, needed them to confirm my place at uni. Nightmare.
You can only get replacements if they were stolen. Otherwise you need to apply for a certificate of representation from each exam board instead. Best thing to do is to contact your school, as you said, to find out which exam boards you took the tests with. If, like me, you get no response then you'll need to apply to each exam board to do a search at around £50 a go.
Some exam boards will give you your money back if they don't find any of your records so it's best to start with those before moving on to ones who will keep your money regardless.