Timing doesn't work.
TFX ordered from GD 12/62 with TF30. On that day small, dry Spey was all RR had, but that was not much (BSEL had everything). During 1963 RN and RR peddled wet Spey/F-4B; RAAF 1963 took F-111C in default of any other high-volume, Pacific-deployed strike type (purge from your mind any notion of Oz TSR.2: why would they take a type that UK vaguely thought of putting on Diego Garcia in quantity 8?).
RN succeeded, 27/2/64 in displacing P.1154/RN (BS.100) for F-4K/Spey 201. Great agitation in UK Govt. that RR would be able to fit reheat in Spey, a) at all, b) in the cascading timescale of F-4 production. But RR gets on with it, as the alternative was to die: they had nothing else...until 2/65 when F-4M was ordered in volume that would really stretch RR and its supply chain.
6/4/65 UK takes F-111K Option for 50 units, 10 with TF30, 40 to be confirmed. Urgent funding released to RR to beef up F-4 Spey for F-111K. 40 so ordered 1/2/67. Allison licence (to be dry TF41) then agreed, and selected for A-7D, as F-111K $ offset. How lucky was UK that US stayed with TF41 even after F-111K was chopped 16/1/68. Spey 201/F-4K seen as fit during 1968 - far too late for DoD to disrupt F-111A/TF30. There was then no basis to foresee that TF41 would ease any of the issues that would tarnish F-111A/C.