Al-Buraq
Banned
No, the RAF wanted P.1154 & TSR-2, The Royal Navy wanted CVA-01, a/k/a the Queen Elizabeth class "supercarrier", at all costs...
As a result of this, the "senior service" effectively sabotaged any programme that was not CVA-01, including P.1154 (which it had ever been built, would have been 2 almost completely different aircraft, with extremely limited communality, with each other's version), TSR-2, the "Thin Wing" improved Buccaneer, capable of Mach 1.2, & even a proposed avionics upgrade for Buccaneer, to ensure that CVA-01 would enter service...
Unfortunately for the Royal Navy, the economic crisis of late 1967-early 1968, ensured that CVA-01 was cancelled...
I think that you have that cart before the horse, or as this is a Navy matter, arse about face. Like their American cousins the British Armed forces were (and still are) more at war with each other than most foreign enemies. Both wanted to have a nuclear deterrent to prove their value ( and, let us not forget, provide the level of importance for very senior officers as far as progression to Chief of Defence Staff is concerned).
Dear Lord Mountbatten was quite prepared to destroy the RAF if he could take the salute from a big ship.
Yes, the RN wanted "real" carriers. They wanted to command "real" carrier strike groups (thus the type-82 destroyers)-- but they also needed something to fly off of it! There was no chance by the mid-1950s of any purpose designed and built naval aircraft and the requirement of multi-role would always provide a compromise. At the time of the CVA-1 planning there was extremely limited choice, apart from the Phantom, there was only the Mirage IIIM outside of the British aircraft industry and by the time the CVA-01s would have been in service, both aircraft, while not totally obsolete, would have been well into middle-age.
The "Super-Buccaneer", the Buccaneer 150 was actually a project for the RAF and a TSR-2 competitor. It was never intended as a Naval aircraft. The plan for an updated Naval Buccaneer never got beyond the back of a fag packet as the design was already considered long-in-the-tooth in the late 1960s, which is ironic in retrospect. You are right that the RNs mission requirements would have made the twin-seat P1154RN more or less a completely different aircraft and therefore financial non-viable fro the RN alone, but look to the eventual export sales of the Harrier/Sea Harrier. Remember the P1154 had won the "Pan-European" VTOL contest.
The choice of the Phantom was basically a choice of that craft or nothing for the RN. In the Naval role it was not the best strike aircraft, not really manouverable enough to be the best top-cover interceptor and considering the attrition of US versions in Vietnam to AA fire, one wonders how it would have performed in its designated RN role of a low-level strike aircraft against well defended targets. But it was better than nothing!