Many thanks Alan. I am immensely grateful. The service number 239935 is definitely correct.
I see that Margaret Wear appears aged 35, born in South Shields, in the 1911 census as "companion" to 84 year old Sarah Proctor, another mystery, but the source
https://www.familysearch.org/ark:/61903/1:1:XWM4-BH8 does not provide the street address. Unfortunately, I no longer have access to Ancestry, so I cannot check the family tree there for Margaret Wear, or contact its owner.
Many thanks too for the link to Arthur Needham, who does seem a likely candidate for John Harold Wear.
I have an undated photograph of the man I believe to be the Wesleyan Methodist minister (possibly Joseph Alfred Needham), posed sitting down and holding an opened book, presumably the Bible. He is dressed in a style that fits the 1920s/1930s. An ordination photo from 1929 perhaps. In a more informal photo, he appears to be with his wife and their baby.
The Oxford Centre for Methodism and Church History at Oxford Brookes University has a collection of photographs of Wesleyan Methodist ministers, but it is closed for the lockdown. I'm sure trying to identify people in old photos is a common problem.
I have not be able to find anything about John Harold Wear's uncle Thomas Hall Reed or to connect him to the Wears you have discovered.