There's probably nothing wrong with the link bushes, although it never hurts to check them. More likely, the spring has simply weakened over the last 27 years. It's very common on the later Spitfires, especially from 1974 on with the rear frame extensions and increasingly heavier rear bumpers, etc., etc.
This is why some folks go with the air shocks, although I personally feel that's a band-aid fix. If the spring is intact (no broken leaves) and if there is a spring shop in your area, you might be able to have it rearched. Alternatively, you might want to go ahead and get a new spring...but get the "heavy-duty" one, which should be a more durable spring. Original Triumph part number for the "stock" spring was 159640 (MkIV) or 159654 (1500 and GT6, according to Canley Classics) or possibly 311539. The last number is what The Roadster Factory currently quotes for all Spitfire MkIV and 1500, and 159654 is what they quote for the late MkIII GT6 (which might also be a good "heavy-duty" spring for a late Spitfire).