Can anybody recommend a book that gives an overview of British India, one that gives a general timeline of the period rather taking a historiographical look or making arguments.

Let me just put these points out there -

Very few books on the British period in India are going to be free of bias.

A colonial bias is the usual state of affairs with British authors till the decolonization period - for example James Mill's notorious book The History of British India. Even today, authors like Niall Ferguson and Lawrence James continue to spread the notion of a benevolent British empire.

A anti-colonial bias is the case with many modern authors who wish to revise the historical bias in Anglocentric history - and this includes most Indian authors, for example Shashi Tharoor's An Era of Darkness (which, while a valuable read, is not academically sound and is written explicitly to counter colonial superiority).

The period of British India spans ~350 years, starting from the Mughal emperor Jahangir's reign and ending after World War 2. It spans the Mughal rule, Maratha empire, Napoleonic Wars, and then the world wars 100 years later! It's rather difficult to package it into a single book.
India is a huge country (more so pre- partition)! It is impossible to create a historical book which can distill everything from Kashmir to Kanyakumari, from Balochistan to Burma without choosing to focus on a smaller area / period.
It is also a very confusing period! If you are familiar with the map of British India - the mess of provinces and princely states that actually constituted British India - you'll realize what I am talking about. Treating India as a monolithic entity doesn't do it justice.

Honestly, as an introduction, Wikipedia is a good resource for an entry-level reader. Just search for terms you seem unfamiliar with. If your complaint is that these books contain 'events that (you are) completely unfamiliar with', don't start by reading academic books!

The second would be reading school level Indian history textbooks (you can find PDFs here), because they will give you a high level overview of various events in Indian history. These books are actually used for reference in the public service examinations in India.

Here are some books:

CA Bayly is one of the pre-eminent voices on British colonial history. His book Indian Society and the Making of the British Empire should be a good fit.
The East India Company: A History by Philip Lawson is an introduction into the period of company rule.
India's Struggle For Independence by Bipan Chandra summarizes the events from the revolt of 1857 to independence very well. As a starting point, it's good for the British Raj period.

It would also help to know India's history in order to place the British in a proper context. For a starter, I would recommend India: A History by John Keay and those textbooks I talked about above.