Given the problem of Britain's overseas empire (far-flung our navies melt away), my fleet construction program would
concentrate on the notion that Britain needs to protect convoys, and have ships available for many stations and possible points
of conflict all over the world.
The core force of BBs/BCs (15 in 1936) can suffice with the addition of a new batch of hardy not-confined-by-treaty battleships.
I would order 4 improved KGVs, basically Lion, with 45,000 tons/30kts/9x16 in, laid down at roughly same pace as the KGVs
were historically, and retain the plans for refits of older BBs/BCs that were under way.
The carrier situation is more problematic. In 1936 Britain had 6 carriers available, of which only 3, Courageous, Glorious, and Furious,
could keep up with the faster battleships. Eagle, ex Chilean Almirante Latore BB, was a nice looking design, and it seems that a good
refit could have enabled an increase in either her speed (from 24kts) or her AC capacity (from 21), to allow her to be able to operate
as a full fleet carrier. Argus is largely fit for training, and Hermes, likewise, is very limited with slow speeds and few aircraft.
Furious I would refit to bring her up to the standards of her 2 sisters with AC complement of 48. Ark Royal had been laid down
in 1936. I would keep that construction going and add 3 others of similar design.
In Sept, 1939, Britain had 66 cruisers active, with 23 new ones laid down. I think the cruiser designs of the Kents, etc, were all
basically sound, and a program extending the 8x8 heavies and 9x6 lights would be sufficient, at a pace consistent with what
was in effect in 1939. Britain had to have a large force of cruisers to protect her overseas stations. I would go for the max possible
here, sacrificing the allowable 6/6 new battleship/cv designs by 2 each. The same with destroyers, DEs, corvettes, or any number
of other smaller ship types. As many as possible would be ideal. The saved 170,000 or so tons from having a 4/4 BB/CV program
instead of 6/6 would applied towards these smaller support warships. 8 capital ships with proper escort to me seems more
reasonable than 12 without, given the number of times RN capital ships were sailing around with little or no escort at all, some of
them being sunk for their efforts.