For short range IR, the problem was the Sidewinder was just so good. It’s basic objective and philosophy of providing a degree of guidance to a cheap 3inch was delivered with clever, elegant, indeed brilliant design which amounted to miniaturisation before the phrase had even been invented. Cheap equals quantity which has a quality all of its own. Sure Firestreak and Red Top offered respectable performance but they’re just uncompetitive in the wider market. Then in the nineties electronic miniaturisation offered more performance and was available to everyone the Sidewinder has gradually lost its exclusivity.
As for radar, the Brits initially went for fire and forget Red Dean but the it’s range was not too different to Sidewinder, ok front aspect, but it was really heavy, expensive and draggy. So semi-active was the way forwards which are inherently launch platform dependent. The only two U.K. produced fighters capable of supporting a capable radar, ie the Sea Vixen and Javelin didn’t make it to the next variant and worthy replacements, ie F155 and P1121, were strangled at birth. It’s not that surprising that nothing really emerged until the tarted up Sparrow aka Skyflash for Tonka F3.