Hi Audrey
Carlisle 1851 is paperbased and in 7 parts - more if you count the outlying districts that form part of the city today.
There is an on-line name index at
http://rolyg.members.beeb.net/CensusNames.htm and you can buy the full transcript booklets from
http://www.cumbriafhs.com/ - prices are not too bad.
Botchergate was (from memory) in parts 3 & 6. 3 is one the on-line name index and I have a copy of the full transcript for part 6. This lists at 3 Baty's Court:
John Sewell H M 28 Shoe Maker CUL Carlisle
Jane Sewell W M 26 CUL Carlisle
whom I think is the wrong John(?). No sign of John & Mary senior in the part I have but possibles for them in part 3 so may be worth getting hold of a copy to check it out.
However there were a lot of cotton mills in Carlisle at the time (see
http://www.stevebulman.f9.co.uk/cumbria/industry.html ) and the family may have moved around the city so probably worth checking out all the possibles on the name index. Maybe a trip to or contact with the record office would be cheaper!
Sue