It seems that the surname of 'Gallagher' that you obtained from baptism record is incorrect and should be Gollagly or Gollogly. I see this was listed on baby Walter's death certificate too.
You needed to stay in Scotland because that is where Walter Bailey married Margaret Gollagly on 8/11/1913 in Glasgow (strange they come up as Walter and Margaret in the index but when you view the certificate it just has 'W' and 'M'. He was 33, son of John Bailey, Ship Plater and Grace, nee Griffiths - both shown as deceased. She is 21, dau. of James Gollagly, Tailor (journeyman) and Helen, nee Mills.
Although they married in Glasgow the address for them both is given as 27a Parkhead Street, Motherwell.
They had a dau. Helen Grace b. and d. 1914 in Govan (named after her respective grandmothers) but knowing that there now seems to be no connection to Lancashire or the name Gallagher I'm wondering if the plain John Bailey b.1915 Govan could be your John.
Annette