Margp - yes, in 1911 he was living with his wife Esther Jane, and his son John Wales Pendleton, and his daughter Edith. He was still a Journeyman Joiner. And no, Margp, I'm not offended by your suggestions!! It is possible, people did and do live double lives. But my dad does remember him very well and knows that he lived with his other daughter Jane who had married Henry Barton, following the death of his wife Esther Jane in 1917. The Bartons lived in Gwyndey Moss Lane, Windle in 1935 when she died.
Also, I have followed the other Peter Pendleton from Windle all through the censuses, and he had a son William, and was a Labourer; so my death certificate is almost certainly his.
Deb - I don't know! I don't think it is him; there's no connection at all to Oldham, and I don't know the name Jane Elizabeth Pendleton; there are John Pendletons in previous generations. The problem is there is a whole other lot of Pendletons from Manchester (Blackley) and they have almost exactly the same names and similar birthdates. I think there must be a connection somewhere but I've never been able to find it.
Jinks - yes I have discounted that Peter P, as my PP was still alive in 1922 and living in Argyle St, St Helens. Also, in each census search there are three Peter Pendletons, two from Prescot and one Peter S Pendleton from Prestwich (sort of near Manchester?!) - in 1911 he is down as Peter Smith Pendleton.
Thanks all of you for your help on this one.