Second piece of the puzzle.
RN ordered the Vickers Supermarine Type 556 (twin seater Scimitar with reheated RA.24R Avons, and a 30 inch AI.18 for Red Dean, or Blue Jay AAMs), in Septemer 1954 to NR/A.38. A single prototype XH451 was ordered and a mockup started to be built.
DH's DH110 had been declared the winner of NA.38 in 1953, but then it had been a contender to the NA.14 issued August 1946, 6 prototypes ordered in April 1949, two for the RAF, two for the night fighter role and two for the strike role. It was expected DH would take 5 years to produce the machine in 1946, and by ordering or prototypes was expected to reach service by 1953.
In a review in 1950 it was realised the DH110 would not be ready before 1956-57. To cover the delay, they went for the SeaVenom, a modified Vampire as an interime solution.
So we can see the RN was hedging its bets with the Type 556 order and viewed that design as having more scope for development than the DH110.
Work on the mockup Type 556 was suspended on 27 April 1955 and the order was canceld in July 1955. Due to the funding constraints of the DH110, NA.39 (B103 Buccaneer) and the oncomming OR.337/Specification F.177 mixed powerplant interceptor, in which Saro's P.177 was recomended on 21 April '55. Though the OR was completed in 17 May 1956, "Mixed Powerplant Interceptor Fighter".
The Admiralty wrote a sister specification NA.47 and Saro was the made the winner.
So we can see they threw away a chance for a moderately decent machine, that could be upgraded for supersonic flight and given ever more powerful engines, with a decent sized radar that by its nature would drive the effort for radar guided AAMs. In favour of the mixed powerplant machine that was smaller, lighter, faster and very nearly the same machine as the RAF where opting for.
Trying to run before they could walk so to speak and in the process they lost both by 1957, with just the DH110 continuing, by that time out of date already, but at least it was funded and working.
Assuming they had carried on the with Type 556, we'd likely see IOC around the very late 50's to early 60's. Weight increases over the existing Scimitar could be handled by increaing the extend of blow over the whole leading edge of the wing countering the overwise increased take off and landing speeds, rather than the partial affair the F.1 had.
Again the spend is both possible and way before the financial crisis of the Wilson government.
It also paves the way for a mk2 version, and removes the degree of urgency that forced the choice the F4K Phantom.
Scimitar F.1 as was, is to NA.19, a sort of barebones, quick and dirty solution until the NA.39 came into service. No reheat, no radar, not even a second seat, and only able to launch with Red Beard, but not land on a carrier with it, rather it had to divert to land. This due to the weapon being 'armed and live' and the wing mounting raising the possibility that it would impact the deck on recovery.