In insurance terms a previous and/or current medical condition is known as a pre-existing medical condition. Not all pre-existing conditions are excluded and some may be covered after an initial stand down period although pre-existing heart, cancer (specific), back, knee and hip condition are generally permanently excluded by most insurers.
Pre-existing conditions are a very complex area and it is well worth your time to sit down with a trained adviser to discuss your personal circumstances and needs. Absolute insurance as a brokerage has been very successful in finding cover for many of its clients with pre-existing medical conditions.