Pre-Independence History covers a very long period which is too large to be covered in entirety in a single book. However, I can recommend a few general histories
- A Survey of Indian History by Sardar KM Panikkar
- A History of India by Burton Stein
- Two Volume Indian History by Penguin Books (Romila Thapar and Percival Spear)
- Indiaby John Keay
None of these books are comprehensive. They were written as general histories and are meant to be introductory on the subject. KM Panikkar’s book was written before many of the recent advances in history and hence is lacking in being up to date. However, it is one of the shortest, sweetest books on the topic. John Keay is not a historian. His book is recommended because it is very enjoyable. He suffers from Western prejudices and notions about India and also lacks in depth in his analysis. The second and third books are highly recommended even though they are a little bit difficult to read.
As for Post Independence period, there are two general histories that cover most aspects.
Of these India Since Independence is a better history book because it is written by a historian trained well in the discipline. Guha is a little shallow in his observations and method. However, his language is much better than Bipan Chandra and makes for a much more engaging read. I think that is the reason for the popularity of that book too.
Enjoy your reading.