Nope there will be no problem if you do LLB degree after BA. In India most of the advocates follow this process only and very less universities actually provides the BA LLB integrated courses. So you don't worry its perfectly fine for you to pursue LLB after BA.

As you know for LLB you have to apply for entrances. The most preferred exam in India for Law is CLAT. This exam is an national level examination and it offers admission to some of the finest and pioneering institute of law in India. Apart from this there are numerous state level and private college examination which you can give as per your aspiration, but I would highly recommend that you should mandatorily gives CLAT examination.

Some of the eminent law colleges in India are:

NLSIU Bangalore - National Law School of India University

NLU Delhi - National Law University

NLU Hyderabad - NALSAR University of Law

For more colleges visit the link provided below:

https://law.careers360.com/colleges/ranking

To know more about CLAT visit the link below:

https://law.careers360.com/exams/clat

For list of law exams in India visit the link provided below:

https://law.careers360.com/exams

I hope this answer helps. All the very best for your future endeavors!