Anti-Kamikaze was UK's first GAAP application, 1944, assigned to spare AWA in 1946. Red Heathen was split in 1949, liberating Army to do fixed SAM with Bristol (to be RAF Regt. Bloodhound 1) and mobile with EE (to be Thunderbird), with fresh suppliers. I think, PMN1 you are right, that before the 1950 Burns/Templer data-exchange, which put BOMARC data on Bloodhound as (to be) Thor ramjet, and Aerojet General licenced motors in Bristol Aerojet, UK could only do little boosters.
US offered licenced BT-1 Terrier in 1951, declined as that would "have a bad effect on UK GW industry" Twigge, Early Devt of (UK)GW, P.164. We proceeded with a bespoke "convoy escort missile ship", adding bow-mounted Blue Slug SSM. Terrier "would not fit" (Chicken? Egg?) In 1957 US offered BT-3 Terrier, declined, even as we were subsuming our Bomb into theirs, because "US might not supply".
Slug 1 went to sea in 1962. Squander, of money and skills, embarrassing many Ministers in Commons grillings. As for sustaining "independent" design capability, I doubt any corporate wisdom flowed from Slug into Dart, Wolf, or anything. (It is good to see, in your Warships1 link, that Terrier, too, had its problems, endangering life and limb. Though we did not know that when we rejected it).