Having never heard of Gate Lane before Chris's post, I identified it to the east of Priory Road. The maps we have been looking at from 1903 show the crossing severed but, even if it was in use, you couldn't get the correct angle on the Workhouse from there. (But thanks Chris for coming over from the Southern Email Group to have a look

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No crossings of the railway are shown on the 1903 map between Priory Road and Tucker Street stations, or on the S&D line towards Glastonbury within range of the workhouse, so that appears to rule out that angle as well.
A further thought that struck me as I thought about this over the last couple of days was that the inclusion of the railway was probably incidental. The important part of the shot was clearly the subjects, but I wouldn't be at all surprised if that building in the background also had some significance. Otherwise, why shoot it there? If it was just a photo of a jolly day's outing, why not have some local place of interest in the backgound, rather than a darn great building and a bit of virtually unidentifiable railway?
It might be easier to identify the building first and then the railway element would fall into place looking at the appropriate map (although that's what I thought I was doing when I suggested Wells in the first place!

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It is also clear from the photograph, by the number of people wanting to cross the line after the gates were re-opened, that the railway is running through a populated area rather than on the edge of one. Once again, Wells fits the bill in principle but in practice the angles don't work, but this again automatically excludes a number of crossings where there is nowhere in particular for anybody to go once they get to the other side.
I thought the point about "minor railways" was worth looking at more closely as well. As we have already mentioned, the WCP would be a prime contender, but looking at the old maps for the three major towns doesn't find anything that jumps out and suggests "our" location.
"Minor railways" might also apply to yards, lines into docks etc, so with that in mind I started to look at non-passenger lines in such places as Portishead, Bristol, Bridgwater, Exeter and Plymouth. Still no joy there for certain, but there was a workhouse in Bridgwater within photographic range of a railway line (now demolished by the way, but also didn't seem to be the right shape for our building), and also a barracks just outside Plymouth Millbay station, but that area would probably have been far too built up even in those days.
Its a pity that this photograph didn't come to light two or three years ago - somebody could have gone and asked Harry Patch if he knew anything about it
