The article mentions the Duke of York and Prince of Wales as already laid down (towards the end) so that's not them. Makes me wonder which ships these are now.
Churchill might have vetoed them when he took over the Admiralty in September. He wanted to concentrate on anti-submarine vessels and felt the resources demanded by battleship construction could be better used in that capacity.
Put my guess down for the Lion and the Temeraire. Started in 1939, stopped in 1940. Per Wikipedia, ordered 2/21/1939. (Two others of the class ordered in August.
They were HMS Anson & HMS Howe, both KGV class, 35,000 ton treaty ships with 10 14” guns.
The UK did complete one final super-battleship, HMS Vanguard. She was commissioned after Germany’s surrender. Displacement was (IIRC) abvout 45,000 tons. She had eight 15” guns, which had originally been manufactured for the Colossus class battleships planned for the 1920’s, but canceled due to the Washington naval treaties. The guns sat in storage for 20+ years.
Vanguard never saw action, and was not in commission very long.
The Carrier was probably HMS Illustrious.