According to a chart in Appendix F of Gathering Storm, At 9/3/39 the British had seven aircraft carriers operational and two under construction. That is more than I would have guessed but it is still a long way from twelve. Also, I would have expected battleships and carriers to be considered apples and oranges, as far as relative worth is concerned. Battleships were still considered the main offensive strikers while aircraft carriers were more of a useful innovation for ASW and support tasks.
Check out this site:
Illustrious Class Aircraft Carriers
Note that at this point in 1938, all four new carriers were under construction, and assuming the Times is a bit out of date, adding the Ark Royal would make five "under construction."
That leaves us to wonder what the old "seven" operational carriers were in 1938. No doubt, as you say, converted coalers & the like...
And I think you suggest the right idea, that these were intended more for anti-submarine warfare -- hugely important, but not the same category as battleships -- rather than anti-battleshipship weapons.
Always interesting to see how they then thought the next war would be fought, verses how it actually turned out...