Okay, thank you everyone, now I'm making real progress, in no small measure due to everyone's help. Thank you all.
I think I have identified the boat the model is based on; ON776 "The Rankin", built in 1935 and served at Aith in the Shetlands from 1935 to 1961, thereafter in the reserve until 1969 and sold in 1970, still in existence.
Here is my reasoning:
Nicholas Leach in "RNLI Motor Lifeboats" supplies a diagram of a 51 foot Barnett with a stern-hung rudder and offers no comment on other arrangements. But Eric Fry (thank you Charlie for sending me back to take a closer look) says "The type of rudder varied as between individual boats, some having the standard type which could be triced up when necessary, while in others the rudder was set into the deadwood." He also offers plans of a boat with the rudder set into the deadwood. So the search was on for a boat which had a rudder set into the deadwood and which had single plate scuppers. Duncan, thank you for alerting me to the fact that these were fitted to some 51 foot Barnetts; also that they can be difficult to pick out of photographs so I would be looking for something very small and unobtrusive.
The great majority of pictures of 51 foot Barnetts I could find online show stern hung rudders. Most shots are taken from the bow, but even so, the steering cover box can very often be made out. It's a hefty item and quite unmistakeable! So far I have managed to find pictures of two boats without the steering cover box; ON 860, "Southern Africa", the last boat built, and ON 776, "The Rankin", the penultimate boat. Now this model cannot be of ON 860 "Southern Africa", because she had no forward shelter and a clear foredeck, but ON 776, "The Rankin" began to look like a possibility. Then close examination of a photo, using digital magic like playing with the colour balance and increasing contrast, revealed the unmistakable outline of a single plate scupper. So "The Rankin" it is and I can order a set of plans for her with a fair degree of confidence now. Thank you for bringing me up to speed and telling me where the plans are held now. I could NOT have done any of this without all the help and encouragement I have received.
As for the origins of this model, there's a fascinating possibility in this forum, from 2011.
http://www.modelboatmayhem.co.uk/forum/index.php?topic=34603.0This shows a 51 foot Barnett model, built plank on frame and, like mine, with engine room detail. Now it could be the same model, except that there are important details which are different. But on the other hand, the odds against there being two such models seem considerable. Either mine has been modified in the course of its life, which is possible; or it was a second build, inspired by the first but never completed.
I'm attaching a bunch of pictures of my model as it stands; of the damaged main shelter (someone, not me, has tried to break out much of the internal structure, heaven knows why), of the detail parts that exist and ALSO a couple from that post of 2011, including an enlargement of the engine room detail for purposes of comparison. The engines look as if it might be just possible to insert a modern 380 type into them in place of the original motors which seem defunct, in which case it might be possible to sail her without having to radically alter the interior.
That's about it; except to add that this "reverse deck camber" thing on boats with relieving tubes instead of scuppers seems to be a fascinating red herring. Photos of ON733 "Mary Stanford" returned to Ballycotton for restoration show her with no side scuppers (so presumably with relieving tubes) but with what are quite definitely conventionally cambered decks.
All for now and again, thank you all for your invaluable help.
John