Hi JM,
I've just sent myself on a wild goose chase trying to find where the above Nathaniel White lived in the censuses.
I eventually found both Great Quebec St and Thornton Place. They are just around the corner from eachother, just off today's Marylebone Road a couple of streets away from the northern end of the famous Baker Street.
Today, Thornton Place appears to be mews cottages behind some lovely large terrace houses. Great Quebec Street, which is now an extension of Upper Montagu St is also a street of lovely huge posh houses. Hardly somewhere that a(n) (ex) pauper would live.

Now I'm doubting that he is the right Nathaniel White.
Of course the street may have become gentrified over the years. I can't be sure of when they were built but the houses look old and I would say they may have been there in the 1840's ....

I will try to investigate further.
It is approximately 1.7 miles from Dean St (Richmond Buildings) to Thornton Place.