I've realised I had a typo in my previous post in the newspaper item about Stephen's death.
...smoking his pie... should have been
...smoking his pipe.... Small typo, big difference.

I've found Stephen's burial as well...
St Margaret, Barking
No. 322
01 Apr 1888
Stephen Attridge
of Barking
58 years
Note: buried in cemetery
Still no sign of Kitty. I have had a look in asylums in census' but didn't find anything.
Also, just to confirm lizdb's reasoning about Isaac Rainbird and Catherine/Kitty Smith. They married in Great Canfield in 1847 and Catherine was a spinster, 19, and the daughter of William Smith.