For others looking, John's First World War army service papers are indexed on Ancestry as Joseph Baines; indeed it does say that at the top of the first page but elsewhere on the same page it says John Baines. He signs J. Baines which doesn't help clarify matters. Other documents in the set add other variations: he is called Joseph John Baines in one place and writes his name as 'Pt Jhon (
sic) Baines' in some correspondence.
He gives his next of kin in 1914/1915 as his brother Sam, Sparken Hill, Worksop and sister Sarah, Watsons Rd, Worksop. His wife Phoebe was still alive then (according to a newspaper article about the death of their son John William Baines in 1917 she was living at 28 Gladstone Street, Worksop)*, so the fact that she isn't listed as his next-of-kin would seem to be significant.
Some correspondence (post-war if I remember rightly) among the father's army papers gives his address as 42 Gladstone Street, Worksop. When I was looking for his sister Sarah on Ancestry, a Sarah Pearson (formerly Baines) popped up in army records in 1917 as wife and next-of-kin of one Joseph Pearson. Joseph & Sarah's address? 42 Gladstone Street, Worksop! So was John Baines living with his sister and brother-in-law? Or maybe just using their address? He's not with them in 1911, unfortunately.
* see this entry from the Nottinghamshire Roll of Honour:
http://www.
nottinghamshire.gov.uk/rollofhonour/People/Details/20604
The deceased son John William Baines has an interesting entry in the Register of Soldiers' Effects (on Ancestry). A payment of £3-6-6 in 1919 is divided between his mother Phoebe and brother Albert E. Then a payment of £10 in 1920 is divided between
Thomas Makin [no relationship stated] and brother Albert E. Baines. So nearly 9 years after the 1911 census it would seem that Thomas Makin was still on the scene.
Sorry that doesn't help at all with your query about where John was in 1911, Julie, but it does look as if John and Phoebe had gone their separate ways by then.