I agree that trying to find both Nelson Street and Nelson Place in the census is a good idea.
This might not be the case with Nelson Place, but sometimes an address which sounds like a street name can actually be a row of houses. I’ve been caught out in the past looking for a “terrace” which has turned out to be in a row of terraced houses on a street with a different name.
It may not be the case for a “Place” but I just thought to mention it in case.