Perth,
What I have is that the North Side of Middlesbrough began in the 1830s, it was the first part of the area that industry here took hold, mainly as a result of coal being shipped from Port Darlington from the Durham coal fields, the railway ended here at the coal staithes which loaded ships to send the coal south, this was on the south bank of the river tees between what is now the transporter bridge and the Newport Bridge, gradually more industry grew until the discovery of ironstone in the Cleveland Hills and then the iron smelting began primarily as a result of the German industrialist Henry Bolkow's vision. gradually the area began to attract people from other areas as the industry grew and more and more iron puddling furnaces were built, housing was needed, the usual back to back hovels and yards and closes, called ginnels elsewhere. this part of the town was known as "the Marsh" The Far Marsh and "over the border" Really just an area of poor housing and ever increasing iron works, each area with a demarcation line of perhaps a road or other unnofficial boundary. All this disappeared in the 1960s when the slum clearances began and they still haven't got it right. We have what could be a fantastic river frontage and the council still fail to make use of such a wonderful resource and quality housing, whereas just a little further upriver Stockton have done a fine job and used the river to it's full advantage. (that's my rant over)
The Teesside Archives in Middlesbrough have a set of maps from the early beginning to 1960s that give the areas and street names.
This is only a thumb nail sketch and condensed, there is much more in the way of books and other publications from the Middlesbrough Archives.
You can also use the Tees Valley Indexes to possibly locate the person you seek from Middlesbrough.
James