The structure and composition of the RN, like any force, will depend on the mission. If the parameters of what the RN is expected to do are altered sufficiently, then there is a possibility.
In the immediate postwar era, it is difficult to lose the carriers, as they are very new and there is not a comparable naval weapons system that can control the sea and strike over long distances.
The window of opportunity would be around the late 1950s. This is when we see the RN start to settle into two sorts of mission - hot war and cold war. Carriers, amphibs and frigates were seen as useful for cold war missions, such as flying the flag.
Removing the capacity for 'cold war' missions that could not be carried out by frigates would involve a much earlier retreat from Empire, particularly East of Suez. This would require a point of departure in the 1940s or early 1950s, such as a complete economic meltdown or similar radical change to what Britain saw as her role in the world.
We would also have to change the role of the RN in regards to ASW in the North Atlantic, which is one driver for persisting with the through deck cruiser even after it's original raison d'etre as an escort cruiser for CVA-01 is gone. That would require Britain to take a backward step within NATO, or even leave the alliance structure.
Some combination of those two circumstances would be required for the RN to totally and utterly get out of the carrier game, and not to explore the helicopter cruiser game as the Italians and French did
In such a case, it is not going to be the same type of force in @, but with a greater number of more capable ships. It would be a very different looking fleet. Without the requirement for a 'cold war' mission, the 4.5" guns are out, and won't be replaced by a US gun that would take a rather larger ship, but rather with ASW missiles or Exocets later on.
Area air defence ships in a non-carrier fleet were not that heavy on the ground at the time, so it is unlikely we'd see something much more capable than a Type 42.
It is difficult to postulate what a fleet would be like without knowing what its mission and area of operation will be.
Like others, I don't see the savings from not having carriers being channeled into the surface fleet; at best, it would go into getting a fifth SSBN, but more likely be cut from defence altogether.
In a situation where the RN doesn't have carriers, I can't see the Falklands happening as there would be no reason to retain an amphibious capacity in such a very different scenario; the butterflies from what I see as the early enough PoD tend to indicate that the Falklands themselves would not be kept; and a purely surface fleet of the type that the ATL RN would likely deploy would lack a lot of the RFA/support ships that are required for such a long range operation.
Many smaller ships are only better than a few larger ones when the larger ones do not bring unique capabilities into play. In this case, those capabilities include carrying a commando and their helicopters or striking a target 500nm away. Up until the mid-late 80s, there aren't any non-aviation assets that can do the latter that aren't nuclear missiles.