British Council in Jubilee Hills has a library and it's arguably one of the most well-stocked libraries out there. Apart from thousands of books, hardbound beauties, and magazines, British Library also offers digital content that you can access from the comfort of your home. The space is quite vast, well-lit, and reminds you of solid university libraries, and they host plenty of events too.
Membership fee: The annual membership costs INR 2,000 and they have other membership options like family, student, corporate, online, etc.