My Surname is different from the one I go by, I didn't find out my dad wasn't my dad until I was 17 (now 20) and my national insurance, bank etc are all in the name I thought it was not my birth cert name. Is this illegal? As I have applied for a loan and they needed ID and my birth cert and they are different.

It's not your fault but your parent(s), but you will still have a lot of work to do. Presumably you want to keep the name you've been using, so you need to go to court (county, district, ask where) to apply for a formal name change. There will be a small fee. It's routine and fast. In the US you give a brief explanation to a judge.

If you wish to use the name on your BC, you will have much more work to do, and it may not be worth the struggle.
I wonder what would happen if you did a typical name change as above, only to your BC name. I imagine it would be accepted, if you explain how difficult alternatives would be.