Key Digital Collections of Primary Sources, Focused on India and Asia:
Relevant to British India and South Asia more generally -
India Office Family History search, for finding birth/marriage/death records of white Britons living in India from 1600-1949 https://indiafamily.bl.uk/ui/home.aspx
Archives of the British Indian Association, founded in the 1850s, precursor to the Indian National Congress (the political party that would eventually secure Indian independence from Britain). Some records from the 19th century. Via the British Library https://eap.bl.uk/project/EAP922/search
SOAS Digital Collections of Primary Sources about South Asia https://digital.soas.ac.uk/rsa
The Collected Works of Mahatma Gandhi, many from the 19th century https://www.gandhiashramsevagram.org/gandhi-literature/collected-works-of-mahatma-gandhi-volume-1-to-98.php
Medical Collection of British India, digitized collection of official British publications dealing with medicine and public health in British India, 1850-1950. Via the National Library of Scotland https://digital.nls.uk/indiapapers/index.html
Archives on Indian Labor, which covers 1931 to now https://indianlabourarchives.org/
The One More Voice project, which works to recover and when possible digitize texts written by colonized people and recognize their contributions to 19th and 20th century histories. Many of the sources here are produced by Africans, but some are by Indian and Caribbean authors. https://onemorevoice.org/materials.html
*Library of Congress Digital South Asia Collection, https://www.loc.gov/collections/south-asian-digital-collection/about-this-collection/
*South Asia Open Archives collection contains over thirty thousand (30,000!) digitized print items. These items include newspapers, serials, and journals; colonial reports, censuses, and government documents; works of art, history, and literature; studies in economics, politics, and social structure; reference works, dictionaries, and so much more! https://www.jstor.org/site/saoa/?so=item_title_str_asc
The 1947 Partition Archive, a non-profit non-governmental organization dedicated to institutionalizing the people’s history of Partition, Independence and World War II in South Asia https://www.1947partitionarchive.org/
Relevant to East Asia -
SOAS Digital Collections of Primary Sources about East Asia https://digital.soas.ac.uk/reas
e-Asia Digital Collection at the University of Oregon Library https://oregondigital.org/collections/easia/
Thomas Manning Archive, a 19thc British traveler to China https://royalasiaticcollections.org/thomas-manning-archive/