Positives:
The name 'Richy'
Thomas aged 5 in 1871, giving him a likely 1866 DOB, which fits exactly with our Thomas Richey
The mysterious link to Mary of Middleboro (does this age match her 1901 census London age?-
EDIT- doesn't seem to fit. 'Mary' age in 1901 is given as 42, 'this' mary is given as 30 in 1871...sadly), remember your idea that maybe TWO Marys? perhaps he brought Mary of Middlesboro and the Thomas Richy to London with him? Long shot!
He was lodging in 1881 in Durham (close kind of) with the 'Morrisons'. I know this hasn't been proven, but I think the age, profession and place of birth as Hampshire are 3 super strong factors for a city hundreds of miles away. Not many men in Durham that fitted that criteria in 1881 I don't think.
Is there any reason to think that Thomas Rich(e)y from whatever location, can
NOT have been a boy 'taken in' by Thomas Hollingsworth? I mean like an orphan etc. it could explain his retaining the last name.
As you say, it may be easier to try and disproof this young Thomas Richy from M/Boro than it would be to justify him??
I'm going to throw in a complete wild card about Thomas RICHEY, which may turn out to be absolutely unconnected but we have run out of leads for London-born candidates for him at the moment. I bear in mind the odd clues pointing to the North-East: the mysterious "Durham connection" and the mention of Middlesbrough in Mary HOLLINGSWORTH's 1901 census entry (tenuous I know).
So, what happened after 1871 to the Thomas listed below? Can he be firmly ruled out as being the Thomas RICHEY we are looking for? (Obviously some major family upheaval would be required!)
1871 census: RG10/4890/15/23
Lower East St, Middlesbrough
Patrick RICHY Head Mar 30 Puddler Ireland
Mary do Wife Mar 30 Ireland
Francis do Son 10 Scholar York Middlesbro'
Thomas do Son 5 Scholar York Middlesbro'