Hi Deborah
I went through Shoreham yesterday, and made a determined effort to see if I could spot anywhere where this photo could have been taken. There is very little of the area that is not now covered by buildings so it is very difficult to say exactly, but I couldn't see any part of town where there would be three hills visible in the background as in the picture. There is a part of the road between Portslade and Shoreham wher you can see two hills, but they didn't look anything like as high as those ones. There may be some perspective distortion, but I doubt it.
If it was Shoreham, I would have thought that the hill to the left would probably have to be the one where Lancing college building is located. Its quite a prominent structure, and would have been visible even from that angle. Although I don't know when that building was built.
Of course, I couldn't see every part of town, and this picture may have been taken in an area and at an angle where housing now stands, but I was on the top deck of a double decker bus and got a pretty clear view of the surrounding area, but nothing seemed to match with this picture.
Hopefully someone with a more intimate knowledge of the town in the past will be able to say yes or no with more authority, but I'd have to say that I don't think this is Shoreham.
Glen