A couple more thoughts Dave ...
If you can find your family in the 1861 and 1871 censuses and they are still living in Brinksway, you can trace the enumerator's route by trawling through their 'neighbours' - this often reveals a landmark which still exists today, helping you to locate where they lived.
As you say, streets often change specially in cities, but you can sometimes get lucky.
I usually compare an old and new map (google maps or microsoft maps are good) with the same map from this site:
www.oldmaps.co.uk (slow to scroll

) where you can often find many of the old place names.
Let me know if you need any help.
