Thanks, everyone for your suggestions. Sorry aghadowey, I should have referred to my earlier attempt to find this elusive lady.
Sarah and Jack had no children, so can't trace back this way.
I believe Sarah would probably have been born in the mid to late 1870s and married in the early 1900s, maybe around 1910.
I have been right through the Lancashire Kershaw/Sarah marriages on FreeBMD and Lancs BMD - there are rather a lot of them in Rochdale and Oldham, the most likely places.
The idea of an obit for Jack sounds hopeful. I'll see what local studies in Oldham can come up with.
Alice Wild was born around 1840 but there are even more Alice Wild marriages in the 1860s. Obviously a popular name, and to be honest I am not absolutely sure that she was Sarah's mother. Just a hunch because of a sampler by someone of that name which was left to us by our Sarah.
touchofmange - I will try to keep hopeful and logical, but I have been trying for years to solve this one. If only I asked my mother more about this when she was alive!

Gillg