Helen,
This info does not neccessarily help if you are not in north-east England.
As far as C1851 goes, we have to be grateful to the Northumberland and Durham Family History Society for their labour of transcribing census pages into Surname Indexes( in alpha order) over a period of several years.
My local library at Blyth, Northumberland ( 35 thou , population) has the following available for me and my like......
...about 50 individual booklets on specific census/parish areas for Northumberland ( and one for County Durham).
.. sets of microfiches holding the same for about 60 areas.
.. microfilm of census pages for about 40 areas.
So if you are looking for someone, and you have no idea where there were in Northumberland... you would start at the beginning and work your way through to the end, hoping to pick up what you want , sooner rather than later.
If you knew where they were, then you would choose that specific index and look for the surname in alpha order
Once you get a hit, you would note the "Piece" and
"Folio" numbers, to enable you to quickly access the appropriate census page to see the whole picture of your "target".
Seeing the census page is wise as the Alpha Surname Indexes contain varying amounts of info....
ie some Newcastle indexes do not show, addresses,relationships, occupations or place of birth,
While other indexes show the lot.
But no index can tell you of other people , living in the same household, who have a different surname from the head of the household.
Newcastle City Library has a wider range of Indexes, covering most parts of the northern part of (old) County Durham, as well as Northumberland.
Darlington Library has over 100 Index books, covering the southern parts of Co Durham and bits of (old) Yorkshire North Riding.
And it will be a similar story in many other libraries and record offices.
I do not know of actual Indexes on line, except for parts of Westgate, Newcastle.
Michael Dixon