Thanks for the replies folks, I will check out the census returns mentioned but as he definitely appears to have died in Wigan, Lancs then we may well be on the right track.
Jomot, that is very interesting, his brother Israel was in the army and was reported as being of bad character and I can find Martha on future census returns so maybe Walter had a similar character to Israel and eventually Martha gave up on him. In 1871 she can be found living in Duck Paddle, Heather, which I think may be a row of farm-worker's cottages. Several of the other Bates brothers are also living there. My Great Grandfather, Thomas was born in Whitwick about 1864 so they obviously lived there at some stage between 1861 their daughter Ann (possibly Frances Ann) was born and and 1871 when Martha is living in Heather with the children.
I think Thomas went on to marry Mary Ann and there was a daughter, Annie although she may have been born before the marriage in about 1882. Mary Ann died before 1919 I think. By this time Thomas was living with my grandmother, Annie Elizabeth Becket nee Prince, Thomas served in the Great War where he suffered shrapnel wounds to his leg. He suffered increasingly great pain as gangrene set in and died in 1937 from this condition I think. (going on what my mum told me about her childhood.)