Aside from the proposed carrier CVA-01, one of the efforts that was supposed to build a stronger British Navy after World War II was a cruiser proposal that would equip both guns and the world's first AA-missile, the sea-cat.
Proposed in the 50s, the cruiser was meant to be Task-Force orientated thus was deemed a high priority project back then. The large (15000t) cruiser ship was supposed to have enough room for an AA missile launcher aft, two gun turrets on the bow and a large array of radars.
The inclusion of guns was in fact a modest decision at the time, as the performance of anti-ship missiles were not at all impressive at the time, and land-attack cruiser missile was then a fiction. In the event of needing shore bombardment and a rare case of direct engagement of the cruiser, the guns were supposed to be useful.
As never weres, in the end the cruiser was cancelled due to cost escalations - the cruiser had grown from a 15000ton design to a 18400ton design despite the admiralty in fact wanted a smaller cruiser that saves cost to build and run. The study of these cruiser proposals and their cancellations would lead to the later guided destroyer designs of the Royal Navy.