Given CVA.03 wouldn't be laid down until about 1974 I think it would fall victim to the 1974 Defence cuts, which would kick the Eagle can down the road by a decade or so. The Eagle would fall victim to the 1981 defence cuts.
That's possible, but I think not for three reasons.
Firstly, as you wrote that CVA.03 would have been laid down in 1974 and the Mason Defence Review was at the end of 1974 beginning of 1975 so the accountants are likely to say that's cancelling her now wouldn't save much money especially if the intention was to maintain a force of 3 strike carriers by keeping Eagle.
Secondly, it's my opinion that CVA.03 would have been laid down in 1973 instead of Invincible and been that bit more advanced which would have strengthened the argument for not cancelling her.
Thirdly, the defence cuts from the cancellation of TSR.2 in 1964 to the Knott Review in 1981 took place because of the state of the British economy. The OP which was expanded by
@Tempest II in Post 28 is only going to happen in a TL where the British economy is in better condition.
I made the POD the Sterling devaluation of 1967 to avoid the cancellation of F-111K and the reduction in Phantom orders. (Although, I could have added that it would have also prevented the cancellation of an order for 15 CH-47A Chinooks that had been ordered to replace the Belvedere and the abandonment of plans to buy 15 C-5A Galaxies to replace the Britannias.) The Sterling devaluation also led to the plan to withdraw from East of Suez to be accelerated from 1975 to the end of 1971 which also means that the strike carriers would be kept until 1975 rather than the end of 1971 leading to Eagle's planned Phantomisation not being cancelled in 1968.
You've made it February 1966 with the non-cancellation of the CVA.01 project and the non-withdrawal of the existing strike carriers without replacement in 1975 and the 1968 non-revision to advance the non-withdrawal to the end of 1971.
IMHO the improvement in the performance of the British economy from 1965 required to make the OP and Post 28 possible knocks the OTL defence cuts back a stage or two. IOTL it was:
1966 Cancel CVA.01 class and scrap the existing strike carriers by 1975
1967 Withdrawal from East of Suez by 1975
1968 Withdrawal from East of Suez advanced to the end of 1971. Plus:
Cuts to the aircraft programme (F-111K, CH-47A, fewer Phantoms, no Galaxies)
Strike carriers to be withdrawn by the end of 1971 and and the Phantomisation of Eagle was cancelled.
1974 Withdrawal of most of the remaining forces outside the NATO area and most of the forces in the Mediterranean area. Plus big cuts to the RAF's transport force and the RN's amphibious capability.
1981 Cut the SSN force from 20 to 17, the helicopter carrier force reduced from 3 to 2 and reduce the number of frigates and destroyers from 60 to 42.
ITTL
1966 Reduction in the strike carrier force from 5 ships to 3 and that 3 CVA.01 class would be completed between 1972 and 1980 to replace Victorious, Ark Royal and Eagle.
1967 no defence cuts
1968 Withdrawal from East of Suez by 1975
1974 no defence cuts
1981 Withdrawal of most of the remaining forces outside the NATO area and most of the forces in the Mediterranean area. Plus big cuts to the RAF's transport force and the RN's amphibious capability.