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There is no BMD event for a W J RIDSDALE in Lincs.  Likely just a space filler in the paper.

The Moulsford Lunatic Asylum was apparently known as Appleferry at some time.  (mentioned in a newspaper article). At a later stage, it was Fair Mile Hospital (near Cholsey).

Hi, welcome to Rootschat! 

Just a few random thoughts for now.

You mention MATHERS... when William MULHOLLAND married John's mother in 1879, she was named as Eliza MADDERS.

In the 1891 census, John is aged 17 and his brother James is 11 -
but in 1881 John was 7 and James was 10 - I suspect he was actually 10 months.

Looking for a birth for him, we find James MULLHOLAND (note the spelling!), and the GRO index gives his mother's maiden name as MADDERS.

Looking for other children, there was a William MULHOLLAND born in 1884 (mother nee MCMANUS) who apparently died in 1885.  Was this another spelling variation?

Then there's Ellen MULHOLLAND born in 1886 (also mother MCMANUS) - I don't see her at all.

As I said, random thoughts.  Perhaps another birth name to search for in Ireland.

Just a casual search, Yorkshire 1911, keyword "slept" found 6 people-
One was "unknown name", "tramp slept in yard"
A family of three (named) "slept in outhouse"
A (named) couple "Casuals, on the road", "slept in barn"

In 1921, nine such people were found in Yorks (all named).

They may be out there, but not necessarily named. 

Sorry