Typerated,
The rumour was the RAF wanted to 'keep up' with the USN/USAF and replace the F4 with F14 or F15....then BAe said 'but we've got a fighter version of Tornado....' and the rest is history. The former, with the AWG-9/AIM-54 combo would have appeared a perfect fit for the 1980s RAF war role of intercepting the Soviet bomber force before it either hit the UK or ReForGer convoys.
Would an upgraded F4 (a la Luftwaffe) been a better bet than the F3? Moot point given the politics, but perhaps our jets were a little more tired than the German ones given their early use as mudmovers?