And here is a more definitive reply.
I telephoned Apple (my new machine still had a few days of telephone support) and spoke to a senior adviser.
He said I should have updated iPhoto from 9.6 to 9.6.1 BEFORE upgrading Yosemite from 10.10.2 to 10.10.3 - as Yosemite 10.10.3, because of "Photos", puts a no-entry sign on all previous versions of iPhoto. So if you can still do this, it's the lightest solution.
He recommended deleting all instances of iPhoto, which I did (of course I kept copies elsewhere), I checked with Spotlight that indeed all copies were gone, and then launched the AppStore - Purchases. This time, for iPhoto, instead of an inoperative grey "UPGRADE" button there was an "INSTALL" button.
This duly installed a new iPhoto 9.6.1.
I had thought it was the presence of the new "Photos" that was stopping the update of iPhoto. Not so, it was the non-recognised iPhoto 9.6.
Many thanks indeed to a particularly helpful Apple Senior Advisor (all in French by the way - I live in Belgium).