Well, I would guess it was pretty well impossible, for the folllowing reasons:
1) Islands are not as permanent as people think. Islands may gain or lose their status as a result of changes in sediment deposition or human engineering work. This is well illustrated by Spurn Point, which may or may not be an island! Currently it is only not an island because of engineering works.
2) What constitutes "inhabitable size"? There are lots of islands on the West Coast of Scotland that no-one now would consider inhabitable, but which have been inhabited in the past for military or religious reasons. Does it mean "an island large enough to support a self-sufficient community" or does it mean "an island big enough to build a shelter on"? I would guess there was a couple of orders of magnitude between the two.
3) Distinguishing islands in a list may be impossible - too many repeated names, so without a detailed location you could be stuck! Lots of "Eilan Dubh" (Black Island) on the west coast of Scotland.
4) What about inland islands, for example, the Isle of Ely? In mediaeval times it was entirely surrounded by impenetrable marshland. Island or not? Other examples include Thanet.
5) Nature is fractal, so there is potentially an infinite number of islands available for enumeration. However, the "inhabitable" requirement limits this - but see 2!
Finally, the answer will be distorted according to one's political view as to what constitutes the "British Isles". Certainly a geographer would agree that the term refers to the archipelago north west of France and on the western side of the North Sea. However, an Irish Republican might argue strongly that there is no way that Ireland is part of the "British" Isles - and I've seen a long debate on exactly this topic in another forum. Yes, as a geographer I think it is specious, but politically? And less controversially, what about the Channel Islands? Are they part of the British Isles or not? WHat about Fair Isle?