The link above goes to search results in HathiTrust (a huge database of digitized books/serials), covering thousands of serials published on India between 1815-1914. Most of these items were published by/for British people. A few gems include:
British Indian Association Papers
"The most important holdings of the British Indian Association, Kolkata. The Association, set up in 1851, was one of the earliest and most important platforms from which Indians engaged with the British in India. Its own records, and its holdings of early newspapers and print material, are an invaluable source for the study of colonial relations in India from mid-19th to early 20th century, and the prehistory of the Indian freedom movement."
Imperial Gazetteer of India (1908-9)
This massive reference set, published 1908-9, is a geographical encyclopedia of British territories in South Asia, including what are now India, Pakistan, Bangladesh, Burma, and other countries. The first several volumes have topical information on subjects like railroads, telegraphs, education, religion, police, jails, and more; the rest of the series is organized alphabetically by location. Note: browsing here works well, but searching for keywords appears to be broken. Search within individual volumes in HathiTrust.
Indian Newspapers & Serials in the CrossAsia Repository
This online repository includes hundreds of issues of newspapers (most in Bengali and/or English) from India in the 1800s-1900s. Note: most issues can only be browsed by date, not full-text searched, so you will need to have a date in mind before browsing.
The British Library keeps the archival records of the India Office (the government administration unit responsible for India), as well as a huge number of other books and serials related to India. Most of this is not digitized, but you can use the archival catalog to find and request copies of specific, small sets of records.