Question Author
I don't know if anyone is watching this one any more or at all interested but here is in effect the bottom line.
To recap: A faulty/weak battery and/or connections would not explain why with a generous boost with jump leads from a running car and replicating the earth connections could not get the starter to turn the second time (it would the first time and then the engine came to life but promptly died again). A fuel problem (pump failure or other) is not indicated as fuel seems to be coming through (the filter is full of it).
I arranged an appointment with an auto electrician who had no obvious suggestion to offer and the car was to be delivered to him today.
I can't explain why but late on Tuesday I decided to have a last try before arranging the transportation to the workshop. This time the starter kept turning after/past the first burst of engine life. I persevered, nurtured the thing along and eventually got the car going and brought it the short distance home. Yesterday and today I drove it around and although it is not running particularly well, it does go. I cancelled today's appointment pending further developments because, unless there is a clear fault, it is impossible to tell that/what if anything is (seriously) wrong.
I am at a loss as to what was up but maybe it will eventually come to light. If this happens again I'll not try to get it going but instead have the auto electrician do his diagnosis.