How will universities know I'm free school meals as a private candidate?

I'm couldn't do my exams last year due to really bad mental health issues, this year I'm taking them privately so I'm not in school anymore. Some unis I want to apply for give contextual offers based on free school meals which I had when I went to school so how would they know?

They know because you'll declare you are (or were in your case) in receipt of free school meals in the ‘More about you’ section of the UCAS application.
Who are you using as your referee? If it's your old school, then you can use their buzzword to link them to your application, meaning that they can use the Adviser Portal to provide agreement that you have been in receipt of Free School Meals in the last six years.
Or is someone else providing your reference?

If you tick the box about FSM, UCAS will check this against the national database. This can mean you dont pay the UCAS application fee, and also many Unis will make lower grade contextual offers to those on FSM. If you are concerned that this doesnt apply to you because you are no longer 'at school', check with UCAS (tel:0371 468 0 468 - open to 6pm weekdays) - I think it does extend over a gap year but they will be able to give you a definite answer.

i was eligible but never claimed will this be in the national data base ?