Is your father named on your birth certificate?
What was the basis of your father's naturalisation?
Do you currently hold an Indian passport?
Do you have any siblings and if so, what are their nationalities?
You have very tenuous claim to a BOC status, verging on non-existent.
Firstly,
BOC citizenship is not passed on from parent to child, except if the child is left stateless. Even then, it is not automatic. The parent would have had to register the birth with the British authorities for the child to get BOC status. If the parent has not done that while the child is a minor, the child does not get BOC status. (See
Section 27 of the BNA 1981).
Secondly, by birth in India to an Indian parent in 1990, you automatically acquired Indian citizenship and hence were not stateless and thus could not acquire BOC status anyway.
In any case, BOC status would not give you the right to live in the UK. Only BOCs who do not hold and have not renounced any other nationality can
register as British citizens. If you currently hold Indian citizenship, as I believe, then you are ineligible to apply for British citizenship under these provisions.
So, I fail to see how the solicitor that you spoke to advised you that you are British citizen by birth. However, I am not a lawyer. It may be best to take a printout of this thread and discuss it with him/her and update us on what s/he advises further.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.