I am a children's Social Worker and my advice would be as above. Contact each Local Authority you know you may have been placed with. You may wait a while for a response. However, Social Workers are very aware that individuals who have been looked after will want to trace their routes, create time lines and generally understand what, why, whom and when. Sadly, records are sometimes lost or destroyed after time, but I think you stand a good chance.
Hopefully you know the name of your old Social Worker? If you do and know which authority they worked for, this may be of help when you make contact with Children's Services.
All the best to you and I really hope you find what you are looking for. Don't give up. it takes a lot of digging for you and them! They will be paper files that will be archived and not easy to find.
PS, they do not have the right to with hold information about you now that you are an adult, unless you are deemed as not having mental capacity (in other words, incapable of making informed decisions about oneself). You will probably be offered the opportunity to read your file alongside a staff member. You will not be able to take it home.
Good luck!!!!