Thank you 'all' for your help so far. Info that I can add if it helps:
All the photos are relations that lived at the time in West Yorkshire - Halifax, Bradford, Keighley and surrounding areas.
I have blown up the first photo best I can and I would say that the shoulder badge does not incorporate a 'T', it certainly has something that stands up-right to one side of the whole badge though.
They are not of the same man, to give a bit of back-ground, the man with the 2 good conduct stripes is the brother of the girl in the first image.
Good point re the trousers/no putees - his trouser do look like serge though?