Both sets of your sources are correct; Polaris caused the dropping of plans to build four carriers under CVA-01, but only the first two ships of the class received serious consideration.

Planning for a new aircraft carrier for the Royal Navy began in January 1960, when the Fleet Requirements Committee (FRC) began considering the size of the new ship. New ships were clearly needed; of the RN's existing carriers, Victorious had been laid down before WWII, while the remaining ships had been laid down shortly before the end of the war. Only Hermes, a smaller ship that could not effectively operate the large new aircraft entering service, was expected to survive past 1975, and she would only last to 1980. Replacing every one of the RN's six carriers, especially with a larger ship, was seen as impossible. During a meeting of the Board of Admiralty, the First Sea Lord stated that the government would likely be able to spend on no more than four new carriers. Planning continued in this vein, with six design studies being presented to the Board by the FRC. In January 1961, the Board required that a new design, agglomerating the features of several of these. It was to be at least 48,000 tons. It was also intended to be primarily a strike carrier, launching attack aircraft armed with nuclear or conventional weapons against enemy targets; with this, it was given the NATO designation for a strike carrier, CVA. Design work converged towards a ship in the 50,000 ton range. This included examination of ships from other navies - the French Foch at a low end and the American Forrestal at the high end. Ultimately, a 53,000 ton design was chosen for further development. The intention was for provisional orders to be placed for steel and machinery for the first ship to be placed in 1963, with construction starting in 1965 to complete by 1970.

In May 1963, the Long Term Programme included four carriers, built to this design. However, the timetable for these ships had been pushed back. CVA-01 was delayed by 10 months, with an additional six months delay for her prospective sister ships. This delay was caused by a lack of funding. The Treasury had assigned £1.6 million to the development of the carrier design, but from the last few months of 1962, was reticent to fund projects that fell under this umbrella. This likely was associated with Polaris; the RN began serious planning for the procurement of Polaris submarines at the same time. The Polaris submarine effort also diverted away a lot of the RN's designers from CVA-01. On the 4th April 1963, a staff requirement for a Polaris submarine was accepted. This rapidly produced a sketch design which was accepted in June. CVA-01's sketch design was accepted a few weeks later, on the 17th July.

Less than two weeks later, on the 30th July, a cabinet meeting cut the planned carrier force to three ships. This appears to be because Polaris had both cut the the available funds for the carrier purchase, and because it could take the carrier's role in Britain's nuclear deterrent. Under the new plan, CVA-01 was to replace Victorious and Ark Royal when they went out of service in the mid 1970s. CVA-02 would replace Eagle and Hermes, and a prospective CVA-03 would replace the remaining ships. In 1964, there was some interest from the Australian Navy about procuring a ship to the design. If they had gone through with this, CVA-01 and the Australian ship would have been ordered in late 1966, to complete in the latter half of 1973. The second British ship, CVA-02, would have been ordered in 1969, with CVA-03 following at an unspecified time afterwards. A Legend for the ship was finalised in December 1965, and a final design submitted to the Board on the 27th January 1966. The Board accepted it, providing its deep thanks to the designers.

However, its days were numbered. The seeds of its downfall had been set in October 1964, when the Labour Party's Harold Wilson became prime minister. The new Labour government faced significant economic problems. Britain's GDP growth was sluggish compared to that of France and Germany. Productivity in British industry was low and inefficiency was high; a lot of Britain's industry was outdated, and there was a lack of capital to invest to bring it up to date. Britain was importing a lot, and exporting little, resuting in a 'balance of payments' issue that might require the government to reduce the value of the pound. In this context, reducing military spending was significant. Britain spent 6.8% of its GDP (£2.141 billion) on defence, compared to an average of 5.5% for other European countries. Reducing spending on the military would free up funds for industrial investment or for social spending. As a lot of military material was purchased from other countries, cutting military spending would also help with the balance of payments directly. Shortly after the election, the new defence minister, Denis Healey, began a review of defence spending.

This review was dominated by interservice rivalry between the Royal Navy and the RAF. The RAF had a number of large, expensive projects that it wanted to keep in operation, which would also be threatened by defence cuts. However, it was more able to accept cuts to these than the Navy was. For example, the RAF's new strike bomber, TSR-2, could be replaced by purchasing the American F-111, a cheaper alternative as it would require less R&D spending. The carrier program could not be so easily replaced. The RAF also attacked the rationale behind the carriers. One of the key roles of the carrier was to provide Britain with the ability to project power 'East of Suez'; in other words, to support British allies and Britain's interests in the Indian and Pacific Oceans with an easily deployable, significant, military force. The RAF produced a set of documents laying out an 'islands strategy', which suggested that this role could be filled by RAF strike aircraft operating from bases on British or friendly territories throughout the region. The documents showed that any likely flashpoint would be within strike range; there are rumours that to do so, they lied about how far east Australia is, but there is no evidence for this. The Navy's carriers were also much less useful in what was seen as the most likely or serious war, that against the Warsaw Pact. There were fears that the carrier was obsolete, with its role being taken by guided weapons and other modern technologies. Finally, the carriers were one of the most expensive projects around. Britain had no shipyards that were big enough to build the ships, and few drydocks for them. There was a lack of designers and a perceived lack of welders for some of the specialised work that needs doing. All of these issues greatly increased the cost of the ships. Polaris was also an expensive project, but one that had broad interservice support. It was clear to the Ministry of Defence that Britain needed a nuclear deterrent. The RAF's V-bombers could not effectively pierce the new Soviet air defences that were coming online. The Skybolt air-launched ballistic missile, which could still make them useful, had been cancelled. Silo-launched ballistic missiles had been investigated, but were far too expensive to consider. Polaris was the only possible option, and cutting it was impossible.

On the 14th February 1966, Healey presented the results of the Defence Review to the Cabinet. The CVA-01 project was to be scrapped, and a variety of other military cuts would be made. Britain would not retain a carrier capability after the last of the WWII-era ships was scrapped in the mid-1970s. The Royal Navy would hand over the 'East of Suez' mission to the RAF, and instead focus more on anti-submarine work in the North Atlantic. By this point, some £3.5 million had been invested in machinery and steel for the new aircraft carriers, mainly for CVA-01.

Of the four carriers planned originally CVA-04 was removed from the plan in 1963. Orders were prepared for CVA-01 and 02, but these were cancelled in 1966. CVA-03 was part of the plan, but never ordered before the cancellation.