As you sound a nice person, Your Parents will not be deported when the UK leaves the E.U. You say they have E.U. Nationality, and have Belgium passports, OUR government has said E.U. Nationals already here will not be deported. Why don't you have a Belgium Passport?
Only your Parents Know their Marriage status whether only one is a Belgium National or both. This is why I say it will be important for your British Parents to adopt you..
If you have other problems.
If it is possible Your Parents may adopt you this will cement your Nationality to that of your Parents. for inheritance purposes should one or both die.
Obviously in todays world You can establish your parentage with Certified DNA. CAB may advise you.
Go to your old school and get certified copies of any attendance at school.copies, get your parents to did out any school photos and your school reports.
Get copies of your Birth birth records, if it was in a hospital ask your mother, for what ever records she has. Did you ever attend a Church or other place of worship here again they may have records, if you are Christian, many babies are Christned again ask your parents.
You need records of you living in the UK.. Ask your parents of how they entered the UK and do they have any evidence , such as a record of you being a child on entry.
Do you have any doctors records You must have had some reason to claim DLA That would have required an examination.
Definitely you should Visit Citizens Advice Bureau.. and what ever else you do. Don't go abroad for a holiday, you might not get back into the UK.
You say you have not worked and claimed DLA in 2012, why has this not continued. You should have claimed whatever because you would have got a credit for National Insurance, You will be asked how did you manage to live with no income.
Having no savings means you may get legal aid to help you. Ask the CAB That should be your first task.
They are both Belguim . They are related by blood and I have been asked to provide birth certificate which I have. Have never done a DNA test mind. I have given every paper that they asked for, getting it sorted by a solicitor of some sort and he asked £2500. Whenever I asked the people that care for me why it's so expensive they say it's because it's such a complex case.
I have indeed been Christned but in Belguim. I am still claiming dla but it's going to be changed some other payment at any time and I have a National Insurance number.
I worry as they have not said that I have a fighting chance or not. Nothing..