I think the answer to your question is more nuanced, OP. British citizenship is not directly relevant, though that together with your DD’s long term residency and the reason for her education abroad may figure into her fees status. (If your family has been settled in India for some time, she will be an Overseas student.)
Economics is one of the most competitive degree programmes in the UK. Your DD’s marks are excellent, but it can be very difficult for even top Home students ( predicted three or four A stars at A level) to get a place on a top programme. I don’t know for sure, but I don’t think these programmes relax their standards much for Overseas students.
@Ceramiq is correct that Cambridge, Oxford and possibly others will require the TMUA. It will be very important, provided the basic requirement of adequate CBSE marks has been met.
Neither Cambridge nor Oxford reject CBSE qualifications, but they both have very high bars. Cambridge Economics requires Further Maths of A level students and says that CBSE Maths does not suffice. The website suggests taking the American AP exam: a grade of 5 on the Calculus BC exam ( the top grade on harder one) suffices. Oxford may want a 95 in CBSE Maths for Economics but DD can research this.
The other top programmes AFAIK include LSE, Imperial, Warwick and UCL. It is worth researching their requirements. Economics is so competitive that I wouldn’t make more than one aspirational or ‘stretch’ application.
This leaves loads of universities with less glamorous but excellent Economics programmes where DD could be a very good fit. There are so many that it is worth considering variables like where she would prefer to live, whether or not she wants a campus university, etc before trying to compile a list of four (or five) choices.
As a former admissions tutor I would advise DD, like everyone, to make one of her choices very safe indeed, yet someplace she would be happy enough to go. This would become her Insurance choice. As her results are known, I mean this in the sense of a safe back up choice. All Economics applicants need one, unless they prefer either to take a gap year or to risk clearing.
I hope this makes sense. Best wishes to DD.