Have you checked out freebmd.org.uk - not sure if these are yours, but a Samuel Graham married Ellen Mahoney SQ 1901 in Wandsworth, London (page 1347, vol 1d ) - is it possible that they lived in London?
There is also John H Graham born SQ 1912 (page 1129, vol 10b) with mother maiden name Mahoney - but this is in Carlisle. Do you know where John was born, in which case you can order his birth certificate and find out more about his parents, as a first step?
I'm trying to find out about my great grandad Samuel Graham but have very limited information. I know that he owned a farm probably in Scotland He was married to Ellen who we think had the maiden name Mahoney Had children called Norah, Nellie, Mary, Robert and John. John was born on 2 July 1912
Sorry for limited info but it's all my nan can remember!