Not encouraging news I'm afraid. It's the response from the FIBIS researcher.
As you live in Australia you are able to access the following websites at your local library.
Familysearch which is free and contains indexes and brief transcriptions of the 70% of the Ecclesiastical records copied sent home to England from India up to 1947 when India gained its independence. The remainder of the ecclesiastical records remain with the churches/missions in India if they still exist.
Findmypast which is a pay to view website and has a small selection of India office records including indexes and digitised records (including that 70% of ecclesiastical records)
FIBIS Families in British India Society which has approximately 1.5 million transcribed records in its database.
BACSA British Association of Cemeteries in South Asia
It is not always possible to find a record of a baptism/marriage or burial but one can sometimes find a newspaper notification of an event if said event was in fact advertised.
Looking through Findmypast there is no evidence that either Walter or Kathleen left a will, neither was there any probate documents for them in the UK.
https://probatesearch.service.gov.uk/#willsThere is no evidence that they had a child named Robert (Henry/W)
I let her know that there was an extensive search for the family of Walter and Kathleen and how we came to be in india. She also gave me a link to search for Wills. Trouble is it only affects Wills after 1996!!
I also mentioned that we've just about exhausted the websites she mentioned.

I do really hope that just by pure luck, someone at the British Library uncovers something. Cheers, Betty