Find 2 year olds grave from 1938?

Hi guys

My dad has been searching for years for the grave of my maternal great uncle. He died in Kensington in 1936 at the age of 2 years old from measles.

The only information we have is his mother’s name, his birthplace and death place with dates.

He passed before my grandmother and her sister were born and their mother did not like speaking of him.

It’s our dream to find his grave before my grandmother and her twin sister pass, but we’ve had no luck.

Does anyone have any recommendations on how we could find him? there are no records on FindAGrave, etc

edit for some additional information- my great uncle’s father abandoned his wife during her pregnancy with all of their money. there has been no trace of him since, no death records or anything.